(b) Find the derivative of f(x) =g'(x) =h' (x) =f'(x) =abababa lobbalmo= (x² + 2) (8æ — 5) by using the product rule. Let g(x) = ² + 2 and h (x) = 8x − 5.vaaㅠ sin (a)√a |a| ㅠ√a aㅠsin (a)sin (a)[11183

Answered: Image /qna-images/answer/aabf235d-4e0c-4908-b877-dd38a21ef482.jpg

Answered: (b) Find the derivative of f (x) = (x²…

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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Let f (x) = x sin x and g(x) = x cos x. (a) Show that f ,(x) = g(x) + sin x and g ,(x) = −f (x) + cos x. (b) Verify that f ,,(x) = −f (x) + 2 cos x and g ,,(x) = −g(x) − 2 sin x. (c) By further experimentation, try to find formulas for all higher derivatives of f and g. Hint: The kth derivative depends on whether k = 4n, 4n + 1, 4n + 2, or 4n + 3.
a. Find the derivative of f(x) = x2 - 5x at x. That is, find f′(x). b. Find the slope of the tangent line to the graph of f(x) = x2 - 5x at x = -1 and at x = 3.
1. Given f(x)= x2 -3x a) Using the definition of the derivative, show that f´(x)=2x-3 b) Use part (a) to write equation of the line tangent to y= x 2-3x at x=3 c) At which x - values, does (x) have horizontal tangent line?
Find the anti-derivative of the following: a.) f(x)=4x1/2-(4/x1/2) b.) f(x)=e2x+sin(4x)+2/x+1/(1-x2)1/2 c.) f(x)= 4x3+3x2+2x+1 d.) f(x)=sec(2x)tan(2x)
2. We look at the function f(x) = e2x + 4x3 defined for all x ∈ R.(a) Show that there exists an inverse function f^-1 to f.(b) Find the derivative of f−1 at point 1, i.e. (f^−1)′(1).
(a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this equation to obtain f' (x) + g' (x) = 0. This implies f'(x) = -g'(x). (b) f' (x) = 2 sin x cos x, and g'(x) = 2(cosx)(-sinx) = -2sin x cos x. So, f'(x) = -g'(x).
3. Find the derivative of (a) f(x) = (x + 2 sin x) (1 – 6 cos x), and (b) g(x) = sin x/ 7x
(A) Find an equation of the tangent line to the graph of f(x)=(4x+1)sin(πx) at the point whose x-coordinate is 1/2.(B) Using logarithmic differentiation, find the derivative off(x)=(e^(-3x) √(2x-5))/(6-5x)^4 .
2) Find the domain of the real-valued function defined as f (x) = arc cos 2x/(1+x^2 )+ log (sin.π/x).?
Find the derivative of the function. y = sin−1(3x + 1) The function y = sin−1(3x + 1) is a composition, and so we must use the Chain Rule, given below, to find the derivative. d dx. [f(g(x))] = f '(g(x))g'(x) For the given function sin−1(3x + 1), the "inside" function is 3x + 1 and the "outside" function is f(x) =
5- When the first derivative of the y = sinx function at x =pi/4 is calculated with the forward finite difference formula for h =pi/12 with accuracy o(h^2), what is the approximate value of the relative error for the derivative value? A) 0,0129 B) 2,8125 C) 0,9325 D) 1,1001 E) 1,9277
find the derivative of y with respect to the appropriatevariable. y = ln (x2 + 4) - x tan-1 ( x/2)

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(b) Find the derivative of f (x) = (x² + 2) (8x − 5) by using the product rule. Let g (x) = x² + 2 and h (x) = 8x – 5. -