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# 2.5 Applying the Power Rule

Sumi Vora

### AP Calculus AB/BCΒ βΎοΈ

279Β resources
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π₯Watch: AP Calculus AB/BC - Introduction to Finding Derivatives
π₯Watch: AP Calculus AB/BC - Practicing Derivative Rules
Since mathematicians are generally pretty lazy, we like to come up with shortcuts to complex formulas. The power rule simplifies the derivative for one of the most common functions in this course: polynomials.Β
Letβs imagine you want to take the derivative of x^n
According to the Binomial Theorem (this is the formula you use when calculating (a+b)^2=a^2+2ab+b^2 ),Β
Thus, d/dx x^n = nx^n-1
Donβt worry -- you wonβt have to understand this proof for the exam. But, if youβre a nerd like me, it can be helpful to know where it comes from. π€Β

## The Power RuleΒ β

 For any differentiable function f(x),d/dx x^n = nx^(n-1)
For the most part, youβll take derivatives using the power rule.Β
Example: Find the derivative of f(x)= x^7
f'(x)= 7x^(7-1) = 7x^6
Browse Study Guides By Unit
πUnit 1 β Limits & Continuity
π€Unit 2 β Fundamentals of Differentiation
π€π½Unit 3 β Composite, Implicit, & Inverse Functions
πUnit 4 β Contextual Applications of Differentiation
β¨Unit 5 β Analytical Applications of Differentiation
π₯Unit 6 β Integration & Accumulation of Change
πUnit 7 β Differential Equations
πΆUnit 8 β Applications of Integration
π¦Unit 9 β Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)
βΎUnit 10 β Infinite Sequences & Series (BC Only)
π§Multiple Choice Questions (MCQ)
βοΈFree Response Questions (FRQ)
πBig Reviews: Finals & Exam Prep