# What is the derivative of F(x) = 1/(x-5)?

Jun 7, 2015

We can use the chain rule here, renaming $u = x - 5$.

The chain rule states that $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \frac{\mathrm{du}}{\mathrm{dx}}$

Also, one law of exponentials states that $\frac{1}{a} ^ n = {a}^{-} n$.

Thus, our new function becomes ${u}^{-} 1$.

Derivating...

$\frac{\mathrm{dy}}{\mathrm{dx}} = - {u}^{-} 2 \cdot \left(1\right)$

Substituting $u$:

$\frac{\mathrm{dy}}{\mathrm{dx}} = - {\left(x - 5\right)}^{-} 2 = - \frac{1}{x - 5} ^ 2$