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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).

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 3CC: If xis large, which function grows faster, f(x)=2x or g(x)=x2?
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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
Step 1

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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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