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For the function y (ƒ−¹) '(11) = - ƒ(x) = x² − x − 5, x ≥ 0.5, find - - df dy 1 y=11

For the function y (ƒ−¹) '(11) = - ƒ(x) = x² − x − 5, x ≥ 0.5, find - - df dy 1 y=11

Calculus: Early Transcendentals
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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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: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.
Let \( f(x) = (2 \sin x + 7 \cos x) \tan^{-1} x \) Find the derivative \( f'(x) = \)
Transcribed Image Text:Let \( f(x) = (2 \sin x + 7 \cos x) \tan^{-1} x \) Find the derivative \( f'(x) = \)
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