What is the power rule?

The power rule is a formula used in calculus to differentiate expressions of the form ( f(x) = x^n ), where ( n ) is any real number. The power rule states that the derivative of ( x^n ) is ( nx^{n-1} ).

This rule is very useful for finding the derivative of polynomial functions, as it allows us to easily differentiate terms that involve powers of ( x ). By repeatedly applying the power rule, we can find the derivative of a polynomial function by differentiating each term individually and then combining the results.

For example, if we have the function ( f(x) = 3x^4 - 2x^2 + 5x ), we can find its derivative by applying the power rule to each term: ( f'(x) = 12x^3 - 4x + 5 ).

Overall, the power rule simplifies the process of finding derivatives of polynomial functions and is an important tool in calculus.