Derivatives Product Rule

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# Derivatives Product Rule - PowerPoint PPT Presentation

By Nathan Mehta Period 4 MACH 5. Derivatives Product Rule. Find the Derivative of f(x)=X 4 [5X-1] 3. f(x)=X 4 [5X-1] 3 Original Equation f ’(x)=4X 3 [5X-1] 3 + X 4 ( 3)(5X-1) 2 (5) Get the derivative of X 4 by using the Power Rule and leave [5X-1] 3 as is

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Presentation Transcript
By Nathan Mehta

Period 4

MACH 5

### DerivativesProduct Rule

Find the Derivative of f(x)=X4[5X-1]3
• f(x)=X4[5X-1]3 Original Equation
• f’(x)=4X3[5X-1]3 + X4 (3)(5X-1)2 (5)
• Get the derivative of X4 by using the Power Rule and leave [5X-1]3 as is
• Then add X4 and get the derivative of [5X-1]3 by using the Package Rule
• Then multiply by the derivative of 5X-1by using the Package Rule
Find the Derivative of f(x)=X4[5X-1]3
• f’(X)= 4X3[5X-1]3 + 15X4 (5X-1)2 Simplify
• f’(X)= X3(5X-1)2 [4(5X-1)+ 15X] Factor
• f’(X)= X3(5X-1)2 [20X - 4 + 15X] Simplify
• f’(X)= X3(5X-1)2 [35X - 4] Simplify