4. Find the partial derivatives andax дуSimplify your results as much as possible.for the following functions z=f(x,y).(a) z=In√x² + y²ey(b) z= x++ sin xyy

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Answered: az 4. Find the partial derivatives and…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Activity 1. Find the 2nd derivative of the even-numbered functions and the 3rd derivative of the odd-numbered ones: 1. f(x) = (x + 2)* %3D x2+ 2 2. y=Tx 3. h(z) = z6 + 3z5 – 4z4 + z3 + 2z? + 9z + 10 Vx2-3 4. f(x) = 5. x= (2t + 1) 2 6. у 3 (6 + 2x- x2 )4 1 7. g(h) = 4Vh3. 8h2 8. x = V6t+ t4 9. y = 6x-2 + 7x-3 – x-4 32 1 10. f(x) = Vx2 – Vx 3Vx5 Activity 2. Find (a) y' by equating the function to y and differentiating it; (b) y' by implicit differentiation; and (c) y" using either of the solved y'. 1. 8xy + 2x*y3 = x3 2. x2 = y2 - x³ + 2y (2²+y)? 3. 3x? 4. (x + 2y)? = 4xy + Vx 5. x3 - y3 = 3
x³ – 2/x + 1 Using quotient rule, which of the following derivatives is true for the function y = 2r (x³ – 2/ī +1) 1 A x4 2x 2x (x³ – 2/ + 1) – x² 3x2 x)(x³ – 2/F +1) -15
(3z)²a² find and simplify f(v@). z+2/a' If f(z)
Let f(x) = 2x³ – x² – 3 1. Find the first derivative of the function. (This function can be easily factored without using the quadratic formula). 6x²-x=0 X (6x-1) X=0) 6x-1= x=1 6x=1 6 2. Where are the relative extrema, if they exist? Show all parts of the analysis necessary to determine these point(s). Label everything you do. f'(x) = 6x²-x 3. Find the second derivative of the function. (This function can be easily factored without using the quadratic formula). 4. Find the inflection point(s), if there are any. Show all parts of the analysis necessary to determine these point(s).
This lable gives some values for the functions f(x), g(x) and their derivatives rW, g'). O -1 -3 2-e 2 2. 3. 3 3-3 -2 4 -5 Use the table to evaluate the following expressions a) (eg)4 b) (f +3g)' (4) c) (g.F)' (0) d) (Fog) () e) (goF)'(2) f) (Đ) (3) Olm
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az 4. Find the partial derivatives and for the following functions z=f(x,y). az ax Simplify your results as much as possible. (a) z=In√x² + y² لام (b) z=x+ + sin xy y