Answer
$\lim\limits_{h\to0}\frac{(x+h)^3-x^3}{h}=3x^2$
Work Step by Step
*Notes: In the question that seemingly contains 2 or more variables, you only need to care about the variable mentioned under $\lim$.
$\lim\limits_{h\to0}\frac{(x+h)^3-x^3}{h}$
$=\lim\limits_{h\to0}\frac{(x^3+h^3+3xh^2+3x^2h)-x^3}{h}$
$=\lim\limits_{h\to0}\frac{h^3+3xh^2+3x^2h}{h}$
$=\lim\limits_{h\to0}\frac{h(h^2+3xh+3x^2)}{h}$
$=\lim\limits_{h\to0}(h^2+3xh+3x^2)$ ($h$ gets cancelled)
$=0^2+3x\times0+3x^2$
$=3x^2$
