Problem 3. Find the derivatives of the following functions:(a) f(x) = cos(evarctan a ), r > 0.(b) g(x) = (arcsin(2x))²,(c) h(x) = x In – x, x > 0.(d) j(x) = x2".1< x <2- -

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Answered: Problem 3. Find the derivatives of 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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1. Consider the function f (x) 1 + 2Vx = (a) Find an expression for the first two derivatives of f(x), i.e. f'(x) and f"(x). Hint: Simplify your expression for f'(x) and f"(x) as much as possible by taking a common denominator. This will help with sections (b) and (c). (b) Using the results from part (a), write down the Taylor expansion of f(x) up to order n = 2 around the point xo = 1. Write the final result in the form a + bx + cx² for some constants a, b and c. (c) Use the results of part (a) to compute the derivative if t = Vx. Write the final result in terms of t only. dt
%ro lli. , N M 4 Y:£9 f(x) = sinx C Select the correct choice (find the *: = derivative of the function below) f'(x) 5/3 f(=) = (1 - + x4 %3D 2/3 (4a3 +) II
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Question 3 Find the derivative of the function v=In(2x³ - 3x) Ay' = 6x² - 3 B. y In(6x²-3) Cy' = D. y' = 1 2x²-3x 6x²-3 3 2x -3x

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Problem 3. Find the derivatives of the following functions: (a) f(x) = cos(evare /arctan x), x > 0. 1 (b) g(x) = (arcsin(2x))², < x < 2° - - (c) h(x) = x ln x – x, x > 0.