How do you differentiate f(x)= e^x/(x-3 ) using the quotient rule?

Jan 25, 2017

$\frac{d}{\mathrm{dx}} \left({e}^{x} / \left(x - 3\right)\right) = \frac{{e}^{x} \left(x - 4\right)}{x - 3} ^ 2$

Explanation:

The quotient rule states that:

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

For $f \left(x\right) = {e}^{x}$ and $g \left(x\right) = x - 3$ we have:

$\frac{d}{\mathrm{dx}} \left({e}^{x} / \left(x - 3\right)\right) = \frac{{e}^{x} \left(x - 3\right) - {e}^{x}}{x - 3} ^ 2 = \frac{{e}^{x} \left(x - 4\right)}{x - 3} ^ 2$