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Mastering Differentiation Rules for Calculus | Learn to Differentiate Functions Easily

Understand and apply differentiation rules like Power Rule, Product Rule, Quotient Rule, and Chain Rule to solve simple and complex equations. Learn how to find derivatives of functions with ease through examples and step-by-step explanations.

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Mastering Differentiation Rules for Calculus | Learn to Differentiate Functions Easily

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  1. Rules for Differentiation By Kimberly Low

  2. Power Rule • The derivative of the function f(x) when f(x)=xⁿ is equal to: • f(x)=xⁿ f’(x)= n(xⁿ⁻¹)

  3. Power Rule cont. SIMPLE EQUATIONS f(x)= x⁵ f(x)=3x⁷ f’(x)=5x⁴ f’(x)=21x⁶

  4. Power Rule cont. • More Complex Equations • f(x)=4x⁷-7x⁵+2x-1 f(x)=x⁸-2x⁶ • f’(x)=28x⁶-35x⁴+2 f’(x)=8x⁷-12x⁵

  5. Product Rule • h(x)=f(x)g(x) • Mathematical version: h’(x)=f(x)g’(x)+g(x)f’(x) • Written out version: The derivative of a function h(x) is equal to the first function [f(x)] times the derivative of the second function [g’(x)] plus the second function[g(x)] times the derivative of the first function [f’(x)].

  6. Product Rule cont. • h(x)= (2x-5)(5x+3) • h’(x)= (2x-5)(5)+(5x+3)(2) Use the rule! • h’(x)=10x-25+10x+6 Multiply it all out! • h’(x)=20x-19 Combine like terms! • *Make a box to help you stay organized!*

  7. Quotient Rule • h(x)= • Mathematical version: h’(x)= • Written differently: h’(x)= • Written out version: The derivative of a function h(x) is equal to the bottom function [f(x)] times the derivative of the top function [f’(x)] minus the top function [f(x)] times the derivative of the bottom function [g(x)], over the bottom function [g(x)] squared.

  8. Quotient Rule cont. • h(x)= • h’(x)= Use the rule! • h’(x)= Multiply! • h’(x)= Simplify!

  9. Derivative of a Number • f(x)=c f’(x)=0 • The derivative of any number, c, is equal to zero. • Example: • f(x)=4 f’(x)=0

  10. Chain Rule • f(g(x)) • Mathematical version: f(g(x))= f’(g(x))*g’(x) • Written out version: The derivative of the function [h(x)] is equal to the derivative of the first function [f(x)] with the second function intact [g(x)], times the derivative of the second function [g(x)].

  11. Chain Rule cont. • h(x) = • h’(x)= 2 (cos x) * (-sin x) • h’(x)= -2sin x cos x • h(x)= (3x-4)⁵ • h’(x)= 5(3x-4)⁴ * 3 • h’(x)= 15 (3x-4)⁴

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