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2.5 Applying the Power Rule

1 min readβ€’january 6, 2021

Sumi Vora

Sumi Vora


AP Calculus AB/BC ♾️

279Β resources
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πŸŽ₯Watch: AP Calculus AB/BC - Introduction to Finding Derivatives
πŸŽ₯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 
Let’s imagine you want to take the derivative of x^n
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According to the Binomial Theorem (this is the formula you use when calculating (a+b)^2=a^2+2ab+b^2 ),Β 
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Thus, d/dx x^n = nx^n-1
Don’t worry -- you won’t have to understand this proof for the exam. But, if you’re a nerd like me, it can be helpful to know where it comes from. πŸ€“Β 

The Power Rule ✊

For any differentiable function f(x),

d/dx x^n = nx^(n-1)

For the most part, you’ll take derivatives using the power rule.Β 
Example: Find the derivative of f(x)= x^7
f'(x)= 7x^(7-1) = 7x^6
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πŸ‘‘Unit 1 – Limits & Continuity
πŸ€“Unit 2 – Fundamentals of Differentiation
πŸ€™πŸ½Unit 3 – Composite, Implicit, & Inverse Functions
πŸ‘€Unit 4 – Contextual Applications of Differentiation
✨Unit 5 – Analytical Applications of Differentiation
πŸ”₯Unit 6 – Integration & Accumulation of Change
πŸ’ŽUnit 7 – Differential Equations
🐢Unit 8 – Applications of Integration
πŸ¦–Unit 9 – Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)
β™ΎUnit 10 – Infinite Sequences & Series (BC Only)
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