Power Rule Practice Problems
These problems follow the power rule for derivatives lesson. They start with single powers and build up to polynomials, roots and tangent slopes.
The rules you need
- Power rule:
for any real . - Constant rule: the derivative of a constant is 0.
- Constant multiple and sum rules: differentiate term by term and keep the coefficients.
- Rewrite first:
, . Expand products and split fractions before differentiating.
Common mistakes to watch for
- Subtracting 1 from a negative exponent wrongly.
, not . - Forgetting to rewrite roots. The power rule only sees
. - Keeping the constant. The derivative of
is 0. - Multiplying derivatives of factors. Expand
first, or use the chain rule later.