# How do you find the derivative of f(x)= (e^(x)-6)/(3x)?

Apr 29, 2017

$\frac{d}{\mathrm{dx}} \left(\frac{{e}^{x} - 6}{3 x}\right) = \frac{{e}^{x} \left(x - 1\right) + 6}{3 {x}^{2}}$

#### Explanation:

Using the quotient rule:

$\frac{d}{\mathrm{dx}} \left(\frac{{e}^{x} - 6}{3 x}\right) = \frac{3 x \frac{d}{\mathrm{dx}} \left({e}^{x} - 6\right) - \left({e}^{x} - 6\right) \frac{d}{\mathrm{dx}} \left(3 x\right)}{3 x} ^ 2$

$\frac{d}{\mathrm{dx}} \left(\frac{{e}^{x} - 6}{3 x}\right) = \frac{3 x {e}^{x} - 3 \left({e}^{x} - 6\right)}{9 {x}^{2}}$

$\frac{d}{\mathrm{dx}} \left(\frac{{e}^{x} - 6}{3 x}\right) = \frac{{e}^{x} \left(x - 1\right) + 6}{3 {x}^{2}}$