Hi, how would you find the derivative of 2x^2|x-1|
This is calc ab but we haven't learned the derivatives of absolute values
let u be a function of x ...
$\displaystyle y = |u|$
$\displaystyle y = \sqrt{u^2} = (u^2)^{\frac{1}{2}}$
$\displaystyle \frac{dy}{dx} = \frac{1}{2} (u^2)^{-\frac{1}{2}} \cdot 2u \cdot \frac{du}{dx}$
$\displaystyle \frac{dy}{dx} = \frac{u}{\sqrt{u^2}} \cdot \frac{du}{dx}$
$\displaystyle \frac{dy}{dx} = \frac{u}{|u|} \cdot \frac{du}{dx}$