# How do you differentiate (2^x)x^2?

Mar 19, 2016

The derivative is $x {2}^{x} \left(2 + x \ln 2\right)$

#### Explanation:

Use ${a}^{x} = {e}^{x \ln a}$.

The function is ${e}^{x \ln 2} {x}^{2}$.

Apply product rule for differentiation.

The derivative is

$\ln 2 {e}^{x \ln 2} {x}^{2} + {e}^{x \ln 2} 2 x$

= $x {e}^{x \ln 2} \left(2 + x \ln 2\right)$

= $x {2}^{x} \left(2 + x \ln 2\right)$