# How do you find the derivative of f(x)=(6-5x)^-1?

Apr 8, 2016

$f ' \left(x\right) = \frac{5}{6 - 5 x} ^ 2$

#### Explanation:

Use the chain rule, where if

$f \left(x\right) = g \left(h \left(x\right)\right)$

then

$f ' \left(x\right) = h ' \left(x\right) g ' \left(h\right)$.

If we say then that $h \left(x\right) = 6 - 5 x$ and $g \left(x\right) = {h}^{-} 1$,

$h ' \left(x\right) = - 5$
$g ' \left(h\right) = - \frac{1}{h} ^ 2 = - \frac{1}{6 - 5 x} ^ 2$

then

$f ' \left(x\right) = \frac{5}{6 - 5 x} ^ 2$