# What is the derivative of (6x-5)^4?

Aug 15, 2015

${y}^{'} = 24 \cdot {\left(6 x - 5\right)}^{3}$

#### Explanation:

You can differentiate this function by using the chain rule for $y = {u}^{4}$, with $u = 6 x - 5$.

This means that you can write

$\frac{d}{\mathrm{dx}} \left(y\right) = \left[\frac{d}{\mathrm{du}} \left({u}^{4}\right)\right] \cdot \frac{d}{\mathrm{dx}} \left(u\right)$

${y}^{'} = 4 {u}^{3} \cdot \frac{d}{\mathrm{dx}} \left(6 x - 5\right)$

${y}^{'} = 4 \cdot {\left(6 x - 5\right)}^{3} \cdot 6$

${y}^{'} = \textcolor{g r e e n}{24 \cdot {\left(6 x - 5\right)}^{3}}$