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If f(x) = √2x + 7, find f'(x). Find f'(1).

If f(x) = √2x + 7, find f'(x). Find f'(1).

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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If ƒ(x) = = √2x + 7, find ƒ'(x). Find f¹(1).
Transcribed Image Text:If ƒ(x) = = √2x + 7, find ƒ'(x). Find f¹(1).
Expert Solution
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.

f\left(x\right)=\sqrt{2x+7}

take derivative

f'\left(x\right)=\frac{d}{dx}\left(\sqrt{2x+7}\right)

f'\left(x\right)=\frac{d}{dx}\left(\left(2x+7\right)^{\frac{1}{2}}\right)

f'\left(x\right)=\frac{1}{2}\left(2x+7\right)^{-\frac{1}{2}}\frac{d}{dx}\left(2x+7\right)

f'\left(x\right)=\frac{1}{2}\left(2x+7\right)^{-\frac{1}{2}}\left(2+0\right)

f'\left(x\right)=\frac{1}{2}\left(2x+7\right)^{-\frac{1}{2}}2

f'\left(x\right)=\left(2x+7\right)^{-\frac{1}{2}}

f'\left(x\right)={\color{Red} \frac{1}{\sqrt{2x+7}}}

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