# How do you differentiate f(x)=1/x+1/x^3 using the sum rule?

Dec 22, 2015

$f ' \left(x\right) = - \frac{{x}^{2} + 3}{x} ^ 4$

#### Explanation:

Find the derivative of each individual part using the power rule:

$\frac{d}{\mathrm{dx}} \left[{x}^{n}\right] = n {x}^{n - 1}$

Thus,

$f ' \left(x\right) = \frac{d}{\mathrm{dx}} \left[{x}^{-} 1\right] + \frac{d}{\mathrm{dx}} \left[{x}^{-} 3\right]$

$f ' \left(x\right) = - {x}^{-} 2 - 3 {x}^{-} 4$

$f ' \left(x\right) = - \frac{1}{x} ^ 2 - \frac{3}{x} ^ 4$

This can also be written as:

$f ' \left(x\right) = - \frac{{x}^{2} + 3}{x} ^ 4$