# Power rule review

Review your knowledge of the Power rule for derivatives and solve problems with it.

## What is the Power rule?

The Power rule tells us how to differentiate expressions of the form $x^n$ (in other words, expressions with $x$ raised to any power):

Basically, you take the power and multiply it by the expression, then you reduce the power by $1$.

*Want to learn more about the Power rule? Check out this video.*

## Differentiating polynomials

The Power rule, along with the more basic differentiation rules, allows us to differentiate any polynomial. Consider, for example, the monomial $3x^7$. We can differentiate it as follows:

*Want to try more problems like this? Check out this exercise.*

## Differentiating negative powers

The Power rule also allows us to differentiate expressions like $\dfrac{1}{x^2}$, which is basically $x$ raised to a negative power. Consider this differentiation of $\dfrac{1}{x^2}$:

*Want to try more problems like this? Check out this exercise.*

## Differentiating fractional powers and radicals

The Power rule also allows us to differentiate expressions like $\sqrt x$ or $x^{^{\frac{2}{3}}}$. Consider this differentiation of $\sqrt x$:

*Want to try more problems like this? Check out these exercises:*