f'(x)?

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October 10th 2012, 03:19 PM
pnfuller

f'(x)?

find f'(x) if it is known that
d/dx [f(2x)]=x²

what does this mean?
October 10th 2012, 03:28 PM
MarkFL

Re: f'(x)?

We are told:

$\frac{d}{dx}(f(2x))=x^2$

Using the chain rule, we find:

$2f'(2x)=x^2$

$f'(2x)=\frac{x^2}{2}=\frac{4x^2}{8}=\frac{(2x)^2}{ 8}$ and so we must have:

$f'(x)=\frac{x^2}{8}$

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