by nathan mehta period 4 mach 5. find the derivative of f(x)=x 4 [5x-1] 3 ff(x)=x 4 [5x-1] 3...

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DERIVATIVES PRODUCT RULE By Nathan Mehta Period 4 MACH 5

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Page 1: By Nathan Mehta Period 4 MACH 5. Find the Derivative of f(x)=X 4 [5X-1] 3 ff(x)=X 4 [5X-1] 3 Original Equation ff’(x)=4X 3 [5X-1] 3 + X 4 (3)(5X-1)

DERIVATIVESPRODUCT RULE

By Nathan MehtaPeriod 4MACH 5

Page 2: By Nathan Mehta Period 4 MACH 5. Find the Derivative of f(x)=X 4 [5X-1] 3 ff(x)=X 4 [5X-1] 3 Original Equation ff’(x)=4X 3 [5X-1] 3 + X 4 (3)(5X-1)

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-1 by using the Package Rule

Page 3: By Nathan Mehta Period 4 MACH 5. Find the Derivative of f(x)=X 4 [5X-1] 3 ff(x)=X 4 [5X-1] 3 Original Equation ff’(x)=4X 3 [5X-1] 3 + X 4 (3)(5X-1)

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