# Question #09fd4

Mar 20, 2017

See below

#### Explanation:

This answer will assume $\log$ is referring to the natural logarithm

Chain rule for composite functions:

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

$\left({\log}^{4} x\right) ' = 4 {\log}^{3} x \frac{1}{x} = \frac{4 {\log}^{3} x}{x}$

If $\log$ is referring to the $\log$ of base $10$, then the derivative is:

$\frac{4 {\ln}^{3} x}{x {\ln}^{4} 10}$