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

Mar 10, 2017

$\frac{\mathrm{df}}{\mathrm{dx}} = - \frac{1 + x}{x} ^ 2 {e}^{- x}$

#### Explanation:

According to Quotient rule if $f \left(x\right) = \frac{g \left(x\right)}{h \left(x\right)}$

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

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

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

$= - \frac{1 + x}{x} ^ 2 {e}^{- x}$