How do you find f'(4) if f(x)=22x?

"How do you find f'(4) if f(x)=22x?" was answered by students like you

ds522stlk

2022-04-17

How do you find f'(4) if

f (x) = 2 \sqrt{2 x}

glanzerjbdo

Beginner2022-04-18Added 13 answers

First find the derivative:

f^{'} (x) = 2 \cdot \frac{2}{2 \sqrt{2 x}} = \frac{2}{\sqrt{2 x}}

consider

\sqrt{2 x}

{(2 x)}^{\frac{1}{2}}

and derive it as a normal power of n where if you have

f (x) = x^{n}

then

f^{'} (x) = n x^{n - 1}

and remember to derive also the argument 2x
(Chain Rule) that gives you simply 2.
then substitute x=4 in it:

f^{'} (4) = \frac{2}{\sqrt{8}} = \frac{2}{2 \sqrt{2}} = \frac{1}{\sqrt{2}}

rationalizing

= \frac{\sqrt{2}}{2}

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