How do you differentiate f(x) = -15 / (4x + 5)^4?

Oct 29, 2016

Answer:

$f ' \left(x\right) = \frac{240}{4 x + 5} ^ 5$

Explanation:

As $f \left(x\right) = - \frac{15}{4 x + 5} ^ 4 = - 15 \cdot {\left(4 x + 5\right)}^{- 4}$

We can do a chain differentiation
$f ' \left(x\right) = - 15 \cdot \left({\left(4 x + 5\right)}^{- 4}\right) ' \cdot \left(4 x\right) '$

$= - 15 \cdot - 4 {\left(4 x + 5\right)}^{- 5} \cdot 4$

$= \frac{240}{4 x + 5} ^ \left(5\right)$