# How do you find the derivative of (x+4)/x?

Mar 30, 2016

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

#### Explanation:

$\frac{d}{\mathrm{dx}} \left(\frac{x + 4}{x}\right) = \frac{d}{\mathrm{dx}} \left(1 + \frac{4}{x}\right)$

As derivative of constant term $1$ is $0$

$\frac{d}{\mathrm{dx}} \left(\frac{x + 4}{x}\right) = \frac{d}{\mathrm{dx}} \left(\frac{4}{x}\right)$ or

$\frac{d}{\mathrm{dx}} \left(\frac{x + 4}{x}\right) = 4 \times - \frac{1}{x} ^ 2 = - \frac{4}{x} ^ 2$