Calculus · Grades 11 to 12
Derivatives
Use the power rule and the product rule.
The idea
A derivative measures the rate of change of a function. The power rule turns x^n into n·x^(n-1).
The product rule applies when two functions multiply: the derivative of u times v is u-prime times v plus u times v-prime. It also works when you expand first.
Worked examples
- How to Use the Power Rule Differentiate f(x) = x^5 with the power rule. Three steps, the exponent rule, and the drop-the-power mistakes to avoid.
- How to Use the Product Rule Differentiate f(x) = x^2(x + 3) with the product rule. Four steps, the u and v labels, and the product mistakes to avoid.
- How to Find a Limit by Factoring Evaluate the limit of (x^2 - 9)/(x - 3) as x goes to 3. Four steps, the 0/0 case, and the cancel mistakes to avoid.
Practice this topic
3 problems with answers.