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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Question
![For the function \( y = f(x) = x^2 - x - 5, \, x \geq 0.5, \) find
\[
\frac{df^{-1}}{dy} \bigg|_{y=11}
\]
\[
(f^{-1})'(11) = \text{\_\_\_\_\_}
\]
Explanation:
This problem involves finding the derivative of the inverse function \( f^{-1} \) at \( y = 11 \). The function is defined for \( x \geq 0.5 \), and it is given by \( f(x) = x^2 - x - 5 \). Use the inverse derivative formula, which relates the derivatives of \( f \) and \( f^{-1} \), to solve the problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e51674d-3d29-4cb4-94ad-529601d10286%2F71e09895-f97f-48b6-a9b9-a3eba626309b%2Fy96446i_processed.png&w=3840&q=75)
Transcribed Image Text:For the function \( y = f(x) = x^2 - x - 5, \, x \geq 0.5, \) find
\[
\frac{df^{-1}}{dy} \bigg|_{y=11}
\]
\[
(f^{-1})'(11) = \text{\_\_\_\_\_}
\]
Explanation:
This problem involves finding the derivative of the inverse function \( f^{-1} \) at \( y = 11 \). The function is defined for \( x \geq 0.5 \), and it is given by \( f(x) = x^2 - x - 5 \). Use the inverse derivative formula, which relates the derivatives of \( f \) and \( f^{-1} \), to solve the problem.
Transcribed Image Text:Let \( f(x) = (2 \sin x + 7 \cos x) \tan^{-1} x \)
Find the derivative \( f'(x) = \)
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