Power rule

The power rule allows one to calculate the derivative of a power of a function in terms of the derivative of the function itself. The power rule states that

${\frac {d}{dx}}(x^{n})=nx^{n-1}$

for all integers $n$. This rule is useful when combined with the chain rule. As an example we can compute the derivative of $f(x)=(\sin(x))^{n}$ as

$f'(x)={\frac {d}{dx}}(\sin(x))^{n}=n(\sin(x))^{n-1}\cos(x)$