Bundle: Calculus, 8th + Enhanced WebAssign - Start Smart Guide for Students + WebAssign Printed Access Card for Stewart's Calculus, 8th Edition, Multi-Term
8th Edition
ISBN: 9781305525924
Author: James Stewart
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 10.R, Problem 22E
To determine
To find:
The slope of the tangent line to the given curve at the point corresponding to the specified value of the parameter
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
(8 points) Let D = {(x, y) | 0 ≤ x² + y² ≤4}. Calculate
==
(x² + y²)³/2dA
by making a change of variables to polar coordinates, i.e. x=rcos 0, y = r sin 0.
x² - y²
(10 points) Let f(x,y):
=
(a) (6 points) For each vector u = (1, 2), calculate the directional derivative Duƒ(1,1).
(b) (4 points) Determine all unit vectors u for which Duf(1, 1) = 0.
Solve : X + sin x = 0. By the false positioning numerical method
Chapter 10 Solutions
Bundle: Calculus, 8th + Enhanced WebAssign - Start Smart Guide for Students + WebAssign Printed Access Card for Stewart's Calculus, 8th Edition, Multi-Term
Ch. 10.1 - 14 Sketch the curve by using the parametric...Ch. 10.1 - 14 Sketch the curve by using the parametric...Ch. 10.1 - 14 Sketch the curve by using the parametric...Ch. 10.1 - 14 Sketch the curve by using the parametric...Ch. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10E
Ch. 10.1 - 1118 a Eliminate the parameter to find a Cartesian...Ch. 10.1 - 1118 a Eliminate the parameter to find a Cartesian...Ch. 10.1 - 1118 a Eliminate the parameter to find a Cartesian...Ch. 10.1 - 1118 a Eliminate the parameter to find a Cartesian...Ch. 10.1 - 1118 a Eliminate the parameter to find a Cartesian...Ch. 10.1 - 1118 a Eliminate the parameter to find a Cartesian...Ch. 10.1 - 1118 a Eliminate the parameter to find a Cartesian...Ch. 10.1 - 1118 a Eliminate the parameter to find a Cartesian...Ch. 10.1 - 1922 Describe the motion of a particle with...Ch. 10.1 - 1922 Describe the motion of a particle with...Ch. 10.1 - 1922 Describe the motion of a particle with...Ch. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - 2527 Use the graphs of x=f(t) and y=g(t) to sketch...Ch. 10.1 - 2527 Use the graphs of x=f(t) and y=g(t) to sketch...Ch. 10.1 - Prob. 27ECh. 10.1 - Match the parametric equations with the graphs...Ch. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - a Show that the parametric equations...Ch. 10.1 - Use a graphing device and the result of Exercise...Ch. 10.1 - Prob. 33ECh. 10.1 - a Find parametric equations for the ellipse...Ch. 10.1 - Prob. 35ECh. 10.1 - Prob. 36ECh. 10.1 - Prob. 37ECh. 10.1 - 3738 Compare the curves represented by the...Ch. 10.1 - Prob. 39ECh. 10.1 - Prob. 40ECh. 10.1 - Prob. 41ECh. 10.1 - If a and b are fixed numbers, find parametric...Ch. 10.1 - A curve, called a witch of Maria Agnesi, consists...Ch. 10.1 - a Find parametric equations for the set of all...Ch. 10.1 - Suppose that the position of one particle at time...Ch. 10.1 - Prob. 46ECh. 10.1 - Prob. 47ECh. 10.1 - The swallowtail catastrophe curves are defined by...Ch. 10.1 - Prob. 49ECh. 10.1 - Prob. 50ECh. 10.1 - Prob. 51ECh. 10.1 - Prob. 52ECh. 10.2 - 12 Find dy/dx. x=t1+t,y=1+tCh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - 36 Find and equation of the tangent to the curve...Ch. 10.2 - 36 Find and equation of the tangent to the curve...Ch. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - 1720 Find the points on the curve where the...Ch. 10.2 - Prob. 20ECh. 10.2 - Prob. 21ECh. 10.2 - Use a graph to estimate the coordinates of the...Ch. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Prob. 27ECh. 10.2 - a Find the slope of the tangent to the astroid...Ch. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Use the parametric equations of an ellipse,...Ch. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Prob. 35ECh. 10.2 - Let R be the region enclosed by the loop of the...Ch. 10.2 - Prob. 37ECh. 10.2 - Prob. 38ECh. 10.2 - Prob. 39ECh. 10.2 - Prob. 40ECh. 10.2 - Prob. 41ECh. 10.2 - 4144 Find the exact length of the curve....Ch. 10.2 - Prob. 43ECh. 10.2 - Prob. 44ECh. 10.2 - 4546 Graph the curve and find its exact length....Ch. 10.2 - 4546 Graph the curve and find its exact length....Ch. 10.2 - Prob. 47ECh. 10.2 - Prob. 48ECh. 10.2 - Use Simpsons Rule with n=6 to estimate the length...Ch. 10.2 - Prob. 50ECh. 10.2 - Prob. 51ECh. 10.2 - Prob. 52ECh. 10.2 - Show that the total length of the ellipse...Ch. 10.2 - Find the total length of the astroid...Ch. 10.2 - Prob. 55ECh. 10.2 - Prob. 56ECh. 10.2 - Prob. 57ECh. 10.2 - 5760 Set up an integral that represents the area...Ch. 10.2 - Prob. 59ECh. 10.2 - Prob. 60ECh. 10.2 - Prob. 61ECh. 10.2 - 6163 Find the exact area of the surface obtained...Ch. 10.2 - 6163 Find the exact area of the surface obtained...Ch. 10.2 - Prob. 64ECh. 10.2 - Prob. 65ECh. 10.2 - Prob. 66ECh. 10.2 - If f is continuous and f(t)0 for atb, show that...Ch. 10.2 - Prob. 68ECh. 10.2 - The curvature at a point P of a curve is defined...Ch. 10.2 - Prob. 70ECh. 10.2 - Prob. 71ECh. 10.2 - Prob. 72ECh. 10.2 - A string is wound around a circle and then unwound...Ch. 10.2 - A cow is tied to a silo with radius r by a rope...Ch. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - Prob. 8ECh. 10.3 - Prob. 9ECh. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Prob. 12ECh. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - Prob. 18ECh. 10.3 - 1520 Identify the curve by finding a Cartesian...Ch. 10.3 - 1520 Identify the curve by finding a Cartesian...Ch. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Prob. 24ECh. 10.3 - Prob. 25ECh. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.3 - Prob. 40ECh. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Prob. 43ECh. 10.3 - Prob. 44ECh. 10.3 - Prob. 45ECh. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - Prob. 48ECh. 10.3 - Prob. 49ECh. 10.3 - Prob. 50ECh. 10.3 - Show that the curve r=sintan called a cissoid of...Ch. 10.3 - Prob. 52ECh. 10.3 - a In Example 11 the graphs suggest that the limaon...Ch. 10.3 - Prob. 54ECh. 10.3 - 5560 Find the slope of the tangent line to the...Ch. 10.3 - Prob. 56ECh. 10.3 - Prob. 57ECh. 10.3 - Prob. 58ECh. 10.3 - Prob. 59ECh. 10.3 - Prob. 60ECh. 10.3 - Prob. 61ECh. 10.3 - 6164 Find the points on the given curve where the...Ch. 10.3 - Prob. 63ECh. 10.3 - Prob. 64ECh. 10.3 - Prob. 65ECh. 10.3 - Show that the curves r=asin and r=acos intersect...Ch. 10.3 - Prob. 67ECh. 10.3 - Prob. 68ECh. 10.3 - Prob. 69ECh. 10.3 - Prob. 70ECh. 10.3 - Prob. 71ECh. 10.3 - Prob. 72ECh. 10.3 - Prob. 73ECh. 10.3 - Prob. 74ECh. 10.3 - Prob. 75ECh. 10.3 - Prob. 76ECh. 10.3 - Prob. 77ECh. 10.3 - Prob. 78ECh. 10.4 - 14 Find the area of the region that is bounded by...Ch. 10.4 - 14 Find the area of the region that is bounded by...Ch. 10.4 - 14 Find the area of the region that is bounded by...Ch. 10.4 - Prob. 4ECh. 10.4 - 58 Find the area of the shaded region. r2=sin2Ch. 10.4 - 58 Find the area of the shaded region. r=2+cosCh. 10.4 - 58 Find the area of the shaded region. r=4+3sinCh. 10.4 - 58 Find the area of the shaded region. r=ln, 12Ch. 10.4 - 912 Sketch the curve and find the area that it...Ch. 10.4 - 912 Sketch the curve and find the area that it...Ch. 10.4 - 912 Sketch the curve and find the area that it...Ch. 10.4 - 912 Sketch the curve and find the area that it...Ch. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - 1721 Find the area of the region enclosed by one...Ch. 10.4 - Prob. 18ECh. 10.4 - 1721 Find the area of the region enclosed by one...Ch. 10.4 - 1721 Find the area of the region enclosed by one...Ch. 10.4 - 1721 Find the area of the region enclosed by one...Ch. 10.4 - Find the area enclosed by the loop of the...Ch. 10.4 - Prob. 23ECh. 10.4 - 2328 Find the area of the region that lies inside...Ch. 10.4 - Prob. 25ECh. 10.4 - Prob. 26ECh. 10.4 - 2328 Find the area of the region that lies inside...Ch. 10.4 - Prob. 28ECh. 10.4 - 2934 Find the area of the region that lies inside...Ch. 10.4 - 2934 Find the area of the region that lies inside...Ch. 10.4 - Prob. 31ECh. 10.4 - Prob. 32ECh. 10.4 - Prob. 33ECh. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Find the area between a larger loop and enclosed...Ch. 10.4 - Prob. 37ECh. 10.4 - 3742 Find all points of intersection of the given...Ch. 10.4 - 3742 Find all points of intersection of the given...Ch. 10.4 - Prob. 40ECh. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - Prob. 43ECh. 10.4 - When recording live performances, sound engineers...Ch. 10.4 - Prob. 45ECh. 10.4 - 4548 Find the exact length of the polar curve....Ch. 10.4 - 4548 Find the exact length of the polar curve....Ch. 10.4 - Prob. 48ECh. 10.4 - 4950 Find the exact length of the curve. Use a...Ch. 10.4 - Prob. 50ECh. 10.4 - Prob. 51ECh. 10.4 - Prob. 52ECh. 10.4 - Prob. 53ECh. 10.4 - Prob. 54ECh. 10.4 - a Use Formula 10.2 to show that the area of the...Ch. 10.4 - a Find a formula for the area of the surface...Ch. 10.5 - 18 Find the vertex, focus, and directrix of the...Ch. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - 18 Find the vertex, focus, and directrix of the...Ch. 10.5 - Prob. 6ECh. 10.5 - Prob. 7ECh. 10.5 - Prob. 8ECh. 10.5 - 910 Find an equation of the parabola. Then find...Ch. 10.5 - 910 Find an equation of the parabola. Then find...Ch. 10.5 - 1116 Find the vertices and foci of the ellipse and...Ch. 10.5 - Prob. 12ECh. 10.5 - Prob. 13ECh. 10.5 - 1116 Find the vertices and foci of the ellipse and...Ch. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - 1718 Find an equation of the ellipse. Then find...Ch. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 - Prob. 21ECh. 10.5 - Prob. 22ECh. 10.5 - Prob. 23ECh. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 - 2530 Identify the type of conic section whose...Ch. 10.5 - Prob. 27ECh. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - Prob. 32ECh. 10.5 - Prob. 33ECh. 10.5 - 3148 Find an equation for the conic that satisfies...Ch. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Prob. 37ECh. 10.5 - Prob. 38ECh. 10.5 - Prob. 39ECh. 10.5 - Prob. 40ECh. 10.5 - Prob. 41ECh. 10.5 - Prob. 42ECh. 10.5 - Prob. 43ECh. 10.5 - Prob. 44ECh. 10.5 - Prob. 45ECh. 10.5 - Prob. 46ECh. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - The point in a lunar orbit nearest the surface of...Ch. 10.5 - A cross-section of a parabolic reflector is shown...Ch. 10.5 - The LORAN LOng RAnge Navigation radio navigation...Ch. 10.5 - Use the definition of a hyperbola to derive...Ch. 10.5 - Prob. 53ECh. 10.5 - Prob. 54ECh. 10.5 - Prob. 55ECh. 10.5 - Prob. 56ECh. 10.5 - Prob. 57ECh. 10.5 - Prob. 58ECh. 10.5 - Prob. 59ECh. 10.5 - Prob. 60ECh. 10.5 - Prob. 61ECh. 10.5 - Prob. 62ECh. 10.5 - Prob. 63ECh. 10.5 - a Calculate the surface area of the ellipsoid that...Ch. 10.5 - Let P(x1,y1) be a point on the ellipse...Ch. 10.5 - Let P(x1,y1) be a point on the hyperbola...Ch. 10.6 - Prob. 1ECh. 10.6 - Prob. 2ECh. 10.6 - Prob. 3ECh. 10.6 - Prob. 4ECh. 10.6 - Prob. 5ECh. 10.6 - Prob. 6ECh. 10.6 - Prob. 7ECh. 10.6 - Prob. 8ECh. 10.6 - Prob. 9ECh. 10.6 - Prob. 10ECh. 10.6 - Prob. 11ECh. 10.6 - Prob. 12ECh. 10.6 - Prob. 13ECh. 10.6 - Prob. 14ECh. 10.6 - Prob. 15ECh. 10.6 - Prob. 16ECh. 10.6 - Prob. 17ECh. 10.6 - Prob. 18ECh. 10.6 - Prob. 19ECh. 10.6 - Prob. 20ECh. 10.6 - Prob. 21ECh. 10.6 - Prob. 22ECh. 10.6 - Prob. 23ECh. 10.6 - Prob. 24ECh. 10.6 - Prob. 25ECh. 10.6 - Prob. 26ECh. 10.6 - The orbit of Halleys comet, last seen in 1986 and...Ch. 10.6 - Prob. 28ECh. 10.6 - Prob. 29ECh. 10.6 - Prob. 30ECh. 10.6 - Prob. 31ECh. 10.R - a What is a parametric curve? b How do you sketch...Ch. 10.R - Prob. 2CCCh. 10.R - Prob. 3CCCh. 10.R - Prob. 4CCCh. 10.R - Prob. 5CCCh. 10.R - Prob. 6CCCh. 10.R - Prob. 7CCCh. 10.R - a Give a definition of a hyperbola in terms of...Ch. 10.R - Prob. 9CCCh. 10.R - Prob. 1TFQCh. 10.R - Prob. 2TFQCh. 10.R - Prob. 3TFQCh. 10.R - Prob. 4TFQCh. 10.R - Prob. 5TFQCh. 10.R - Prob. 6TFQCh. 10.R - Prob. 7TFQCh. 10.R - Prob. 8TFQCh. 10.R - Determine whether the statement is true or false....Ch. 10.R - Prob. 10TFQCh. 10.R - Prob. 1ECh. 10.R - Prob. 2ECh. 10.R - Prob. 3ECh. 10.R - Prob. 4ECh. 10.R - Prob. 5ECh. 10.R - Prob. 6ECh. 10.R - Prob. 7ECh. 10.R - Prob. 8ECh. 10.R - Prob. 9ECh. 10.R - Prob. 10ECh. 10.R - Prob. 11ECh. 10.R - Prob. 12ECh. 10.R - Prob. 13ECh. 10.R - Prob. 14ECh. 10.R - Prob. 15ECh. 10.R - Prob. 16ECh. 10.R - Prob. 17ECh. 10.R - Prob. 18ECh. 10.R - Prob. 19ECh. 10.R - Prob. 20ECh. 10.R - Prob. 21ECh. 10.R - Prob. 22ECh. 10.R - Prob. 23ECh. 10.R - Prob. 24ECh. 10.R - Prob. 25ECh. 10.R - Prob. 26ECh. 10.R - Prob. 27ECh. 10.R - Prob. 28ECh. 10.R - At what points does the curve...Ch. 10.R - Prob. 30ECh. 10.R - Find the area enclosed by the curve r2=9cos5.Ch. 10.R - Prob. 32ECh. 10.R - Prob. 33ECh. 10.R - Prob. 34ECh. 10.R - Prob. 35ECh. 10.R - Find the area of the region that lies inside the...Ch. 10.R - 3740 Find the length of the curve. x=3t2,y=2t3,0t2Ch. 10.R - Prob. 38ECh. 10.R - 3740 Find the length of the curve. r=1/,2Ch. 10.R - Prob. 40ECh. 10.R - 4142 Find the area of the surface obtained by...Ch. 10.R - Prob. 42ECh. 10.R - Prob. 43ECh. 10.R - Prob. 44ECh. 10.R - Prob. 45ECh. 10.R - Prob. 46ECh. 10.R - Prob. 47ECh. 10.R - Prob. 48ECh. 10.R - Prob. 49ECh. 10.R - Find an equation of the parabola with focus (2,1)...Ch. 10.R - Prob. 51ECh. 10.R - Prob. 52ECh. 10.R - Prob. 53ECh. 10.R - Prob. 54ECh. 10.R - Prob. 55ECh. 10.R - Prob. 56ECh. 10.R - In the figure the circle of radius a is...Ch. 10.R - A curve called the folium of Descartes is defined...Ch. 10.P - The outer circle in the figure has radius 1 and...Ch. 10.P - a Find the highest and lowest points on the curve...Ch. 10.P - What is the smallest viewing rectangle that...Ch. 10.P - Four bugs are placed at the four corners of a...Ch. 10.P - Show that any tangent line to a hyperbola touches...Ch. 10.P - A circle C of radius 2r has its center at the...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Solve: X + sin X = 0 by the false positionining numerical methodarrow_forwardOn from the equation: 2 u = C₁ + C₂ Y + Czy + Cu y³ Find C₁, C₂, C3 and Cy Using these following Cases : (a) 4=0 at y=0 (b) U = U∞ at y = 8 du (c) at Y = S ду --y. ди = 0 at y = 0 бугarrow_forwardTips S ps L 50. lim x2 - 4 x-2x+2 51. lim 22 - X 52. 53. x 0 Answer lim x 0 lim 2-5 X 2x2 2 x² Answer -> 54. lim T - 3x - - 25 +5 b+1 b3b+3 55. lim X x-1 x 1 Answer 56. lim x+2 x 2 x 2 57. lim x²-x-6 x-2 x²+x-2 Answer-> 23-8 58. lim 2-22-2arrow_forward
- Write a formula for the function g that results when the graph of the function f(x) = = 4 X is reflected about the y-axis, horizontally compressed by a factor of 2, shifted 7 units left, reflected about the x-axis and shifted 3 units up. g(x): = Question Help: Message instructorarrow_forwardQuestion 7 4 pts 1 Details The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x) = 1.8208e0.3387x, where x = 0 corresponds to 1998. In what year did/will the exports reach $10.4 billion?arrow_forwardQuestion 7 4 pts 1 Detai The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x) = 1.8208e 0.3387x, where x = 0 corresponds to 1998. In what year did/will the exports reach $10.4 billion?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Chain Rule dy:dx = dy:du*du:dx; Author: Robert Cappetta;https://www.youtube.com/watch?v=IUYniALwbHs;License: Standard YouTube License, CC-BY
CHAIN RULE Part 1; Author: Btech Maths Hub;https://www.youtube.com/watch?v=TIAw6AJ_5Po;License: Standard YouTube License, CC-BY