find f'(x) if it is known that

d/dx [f(2x)]=x^{2}

what does this mean?

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- Oct 10th 2012, 03:19 PMpnfullerf'(x)?
find f'(x) if it is known that

d/dx [f(2x)]=x^{2}

what does this mean? - Oct 10th 2012, 03:28 PMMarkFLRe: f'(x)?
We are told:

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

Using the chain rule, we find:

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

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

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