# How do you differentiate f(x)=1/(2x+5)^5  using the chain rule?

Nov 7, 2015

$- \frac{10}{2 x + 5} ^ 6$

#### Explanation:

The equation can be rewritten as ${\left(2 x + 5\right)}^{-} 5$.
Now, use chain rule to differentiate:

$\frac{d}{\mathrm{dx}} \left(f \left(g \left(x\right)\right)\right) = f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$

$- 5 {\left(2 x + 5\right)}^{-} 6 \cdot 2$

Simplify:

$- 10 \cdot {\left(2 x + 5\right)}^{-} 6$

$- \frac{10}{2 x + 5} ^ 6$