# How do you differentiate f(y) = e^y /y?

Jun 18, 2016

$\frac{\mathrm{df}}{\mathrm{dy}} = {e}^{y} \left(\frac{y - 1}{y} ^ 2\right)$

#### Explanation:

We use quotient rule here. According to quotient rule

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

$\frac{\mathrm{df}}{\mathrm{dx}} = \frac{h \left(x\right) \cdot g ' \left(x\right) - g \left(x\right) \cdot h ' \left(x\right)}{h \left(x\right)} ^ 2$

As $f \left(y\right) = {e}^{y} / y$

$\frac{\mathrm{df}}{\mathrm{dy}} = \frac{y \times {e}^{y} - {e}^{y} \times 1}{y} ^ 2$

= ${e}^{y} \left(\frac{y - 1}{y} ^ 2\right)$