Question 5 Let sin 7rx cos 18ry = sin 7rx + cos 18my be the equation of a curve in the zy-plane. Find the equation y = T(2) of the tangent line at (0,), then evaluate T(18). T(18) be

Q: Question 12 If y = e^(x^2), then it can be shown that dy/dx = 2xe^(x^2). Using this, lim x→−1…

A: The objective is to find the limit limx→-1 ex2-ex+1. Use L'hopitals rule, that is differentiate the…

Q: What is the corresponding period and phase shift of the function f(t) = cot (2t - Tt)? *

A: Given that  f(t)=cot(2t-π) To find the period and phase shift

Q: What is the equation of the line tangent to the curve e" + cos(x) = 1 at the point C.0. y =1- ... A…

A: Given; ey+cosx=1 at point (π/2,0).

Q: The function y = sin x completes one period on the interval 30, 2π4, the function y = sin 2x…

A: Consider the function y = sinx and its Graph:

Q: b) Use the definition of the derivative to find the derivative of f(x) = 4x³ + - at a = 1. 23

A: Given: fx=4x3+1x3; x=1 We know that ddxxn=nxn-1                                          ..1

Q: Example: show that u(t)=sin t i + cos t j+ 5k has constant length and is orthogonal to its…

A:

Q: Find equation of the tangent line T equals pi divided by six at X(T) equals nine cosine t and  Y(T…

A: x(t)=9cost y(t)=5sint t=π/6

Q: a) Find the points at which the tangent line to the graph of function f(x) =x³ – 36x+60 has slope…

A:

Q: 1. Find the derivative of the curve given by the equation: 2(x - y) = 3+ siny

A: As per our guideline we are supposed to answer only one question you can repost other questions in…

Q: (B): Find the tangent equation to the curve y = sin² x at point x =

A:

Q: y = cot (c*) Arc cos (1-2x)²

A: Explained below

Q: 26 Find the 155th derivative of (1 + x°)" at x = 0.

A: see 2nd step.

Q: Find the derivatives using Trigonometric Functions 4 y = cos* t – sin* t \1/2 ソ= v = (2 tan² 20 –1)"

A:

Q: What is the derivative of 0.50 sin 2t+0.30 cos t

A:

Q: b) Find derivative of the following: 1. y= 5x° + 2x -x + x* -9x+12 y=1-cos 20+3sine iI. ii. s= xln…

A: The detailed solution is as follows below:

Q: for the function y cot V8- 22 dz dy The derivative

A:

Q: What are the derivatives of sin g(t), cos g(t), and tan g(t)?

A: we have to find the derivatives of sin g(t), cos g(t), and tan g(t)

Q: How do I find the following derivatives?

A: Using 1 rules of log 2 derivatives of composite functions (chain rule)

Q: Find y′ if y = (cot(x))sin(x)

A:

Q: 1. If Y= 4 cos x + sin 2x, what is the slope of the curve when x=2.

A:

Q: 3. Find the equation of the tangent line to sin-(x - 2y) = 2ry- 1 at the point (1,

A:

Q: Question 21 Find the equation of the tangent line to y = x = 1. at A y - Vi = - Vi (x – 1) B VE (x -…

A:

Q: y = x. Find y''(1) = r8

A:

Q: y = (1–4 x+ 7x')30

A: If a function is given, y=f(ax+b) then it's derivative will be given as,…