Can anyone help me find the derivative of y=2^|x|?
Hi nejikun.
$\displaystyle y\ =\ 2^{|x|}\ =\ e^{(\ln2)|x|}\ =\ e^u$ where $\displaystyle u=(\ln2)|x|$
So, using the chain rule, $\displaystyle \frac{dy}{dx}\ =\ \frac{dy}{du}\,\frac{du}{dx}\ =\ e^u\cdot(\ln2)\frac{|x|}x\ =\ \frac{(\ln2)|x|}x2^{|x|}.$
Note that $\displaystyle \frac{d\left(|x|\right)}{dx}=\frac{|x|}x.$