1. ## f'(x)?

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

what does this mean?

2. ## 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:

$f'(x)=\frac{x^2}{8}$
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}