# How do you differentiate f(x) = 1 + 1/x + 7/x^2 + 1/x^3?

Sep 26, 2015

Have a look:

#### Explanation:

You can write your function, using the Rule of Exponents, as:
$f \left(x\right) = 1 + {x}^{-} 1 + 7 {x}^{-} 2 + {x}^{-} 3$

and differentiate as ${x}^{n}$ which gives you $n {x}^{n - 1}$, to get:

$\frac{\mathrm{df}}{\mathrm{dx}} = 0 - {x}^{-} 2 - 14 {x}^{-} 3 - 3 {x}^{-} 4 = - \frac{1}{x} ^ 2 - \frac{14}{x} ^ 3 - \frac{3}{x} ^ 4$