How to apply power rule for derivatives

The power rule for derivatives is all about the exponent

The power rule is the tool you’ll use most frequently when finding derivatives. The rule says that for any term of the form ???ax^n???, the derivative of the term is

???(a\cdot n)x^{n-1}???

Hi! I'm krista.

To use the power rule, multiply the variable’s exponent ???n???, by its coefficient ???a???, then subtract ???1??? from the exponent. If there’s no coefficient (the coefficient is ???1???), then the exponent will become the new coefficient.

Using power rule to differentiate a power function

Example

Find the derivative of the function.

???f(x)=7x^3???

Applying power rule gives

???f'(x)=7(3)x^{3-1}???

???f'(x)=21x^2???

To use power rule, multiply the variable’s exponent by its coefficient, then subtract 1 from the exponent.