g(x) = 3 sin x - cos x5. Use the chain rule to compute the derivatives.a)f(x) = sin²x = (sin x)²b)f(x) = sin(x²)c)f(x) = (x4 + 5)³d)f(x) = √√7x-exe)f(x) = ecosx3 sin xd7* COS Xddr

Answered: Image /qna-images/answer/29f6fb07-a239-48a0-b853-57d7554ffe79.jpg

Answered: 5. Use the chain rule to compute the…

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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Differentiate the functions. a) f(x) = 2 – 5x +?x 4 b) f(x) = e* +. c) f(x) = cosx d) f(x) = (5 – x²)· e*
1. Prove that the derivative of tan(x) is sec²(x) directly from the definition of the derivative. You may not use the formula for the derivatives of sine or cosine. Hint: use the sum formula: and the identity: tan(x + y) = tan(x) + tan(y) 1 tan(x) tan(y) 1 + tan²(x) = sec²(x).
A student takes the derivative of the function h(x) = (x² + sin (x) )(1 − cos (x) ) as follows: h(x) = (2x + cos(x)) sin(x) Is this correct or not? Explain what the student did, and if not correct, write down the correct derivative.
2. Computing Derivatives; Compute each derivative using the derivative rules: d cos-"(1+ x²) + tan (a) dx -'(1 + c*) e3x² d (b) (cos(1+x²) + tan'+e3=² da d (c) (1+ x² + ln[1 +x + sin¬'(1 + x)]) dx
Use the product rule to find the derivative of the function. y=(3x²+5) (2x-5) What is the correct way of writing the derivative of y? dy d OA. (3x²+5) (2x-5) dx (3x²+5)•(2x-5) = (3x² +5) • (2x-5) + (2x-5) • (3x²+5) dy O B. dx dy O c. dx dy d ( = (3x² +5) • (2x-5) + (2x-5)•(3x²+5) ○ D. dy dx dx = 則 dx d dx dx d d dx - (3x² +5) • 1x (2x-5)+ + (2x-5) • (3x²+5) dx dx
given that f(x)= 3 sin (2x-30). Draw a graph for f(x)^-1.

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5. Use the chain rule to compute the derivatives. a) f(x) = sin²x = (sin x)² b) f(x) = sin(x²) c) f(x) = (x4 + 5)³ d) f(x) = √√7x-ex e) f(x) = ecosx