# How do you find the derivative of e^(4x)/x?

##### 1 Answer
Feb 24, 2017

$\frac{\mathrm{df}}{\mathrm{dx}} = {e}^{4 x} / {x}^{2} \left(4 x - 1\right)$

#### Explanation:

We can use quotient rule, which states that

if $f \left(x\right) = \frac{g \left(x\right)}{h \left(x\right)}$

then $\frac{\mathrm{df}}{\mathrm{dx}} = \frac{\frac{\mathrm{dg}}{\mathrm{dx}} \times h \left(x\right) - \frac{\mathrm{dh}}{\mathrm{dx}} \times g \left(x\right)}{h \left(x\right)} ^ 2$

Here we have $f \left(x\right) = {e}^{4 x} / x$, where $g \left(x\right) = {e}^{4 x}$ and $h \left(x\right) = x$

and therefore $\frac{\mathrm{df}}{\mathrm{dx}} = \frac{4 {e}^{4 x} \times x - 1 \times {e}^{4 x}}{x} ^ 2$

= ${e}^{4 x} / {x}^{2} \left(4 x - 1\right)$