# How do you differentiate f(x)= e^x/(x-7 ) using the quotient rule?

Jan 15, 2016

$f ' \left(x\right) = \frac{\left(x - 6\right) {e}^{x}}{x - 7} ^ 2$

#### Explanation:

Quotient rule states that

$\frac{d}{\mathrm{dx}} \left[f \frac{x}{g} \left(x\right)\right] = \frac{g \left(x\right) \cdot f ' \left(x\right) - f \left(x\right) \cdot g ' \left(x\right)}{g \left(x\right)} ^ 2$.

Application to the given examples yields

$f ' \left(x\right) = \frac{\left(x - 7\right) {e}^{x} + {e}^{x}}{x - 7} ^ 2$