TOPIC
MY PROGRESS
Pug Score
0%
Best Streak
0 in a row
Study Points
+0
Overview
Practice
Watch
Read
Quiz
Next Steps
Get Started
Get unlimited access to all videos, practice problems, and study tools.
Back to Menu
Topic Progress
Pug Score
0%
Videos Watched
0/0
Best Practice
No score
Read
Not viewed
Best Quiz
No attempts
Best Streak
0 in a row
Study Points
+0
Overview
Practice
Watch
Read
Quiz
Next Steps
Overview
Power Rule for Derivatives
The power rule is the fastest way to differentiate any power of x. See the formula, why it works, and step by step examples.
What You'll Learn
The power rule states that the derivative of x to the power n is n times x to the power n minus 1.
It works for any real number exponent, including negative and fractional powers.
Constant multiples pass straight through, so the derivative of a times x to the n is a times n times x to the n minus 1.
The derivative of a lone constant is always zero because it has no x term to bring down.
Repeated use of the power rule leads directly into higher order derivatives and, for composite expressions, the chain rule.
What You'll Practice
1
Differentiating power functions with integer exponents
2
Finding derivatives of functions with negative and fractional exponents
3
Converting radicals and rational expressions to power form before applying the power rule
4
Differentiating long polynomial expressions with multiple terms
Why This Matters
Mastering the power rule is essential for all future calculus work. It's the most efficient differentiation tool you'll use daily in calculus, physics, and engineering. This rule transforms what would be tedious limit calculations into simple algebraic steps, making advanced problem-solving accessible.
This Unit Includes
12 Video lessons
Practice exercises
Learning resources
Skills
Power Rule
Derivatives
Polynomials
Exponents
Rational Functions
Radical Functions
Constant Multiple Rule
ON Curriculum Aligned