# Prove that the derivative of (e^(4x)/4-xe^(4x) ) = pxe^(4x)  and find p?

Sep 25, 2017

$p = - 4$

#### Explanation:

Differentiating wrt $x$ and applying the product rule, and chain rule we get:

$\frac{d}{\mathrm{dx}} \left({e}^{4 x} / 4 - x {e}^{4 x}\right) = \frac{d}{\mathrm{dx}} \left({e}^{4 x} / 4\right) - x \left(\frac{d}{\mathrm{dx}} {e}^{4 x}\right) - \left(\frac{d}{\mathrm{dx}} x\right) \left({e}^{4 x}\right)$

$\text{ } = \frac{d}{\mathrm{dx}} \left(\frac{4 {e}^{4 x}}{4}\right) - x \left(4 {e}^{4 x}\right) - \left(1\right) \left({e}^{4 x}\right)$

$\text{ } = {e}^{4 x} - 4 x {e}^{4 x} - {e}^{4 x}$

$\text{ } = - 4 x {e}^{4 x}$

$\text{ } = p x {e}^{4 x}$, where $p = - 4$