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Calculating Derivative – A multiplication of polynoms – Exercise 6349

Exercise

Find the derivative of the following function:

f(x)={(3x-1)}^2\cdot{(x+1)}^3

Final Answer


f'(x)=3(3x+1){(x+1)}^2(5x+1)

Solution

f(x)={(3x-1)}^2\cdot{(x+1)}^3

Using Derivative formulas and the multiplication rule in Derivative Rules, we get the derivative:

f'(x)=2(3x-1)\cdot 3\cdot{(x+1)}^3+{(3x-1)}^2\cdot 3\cdot{(x+1)}^2\cdot 1 =

One can simplify the derivative:

=3(3x+1)\cdot{(x+1)}^2\cdot (2x+2+3x-1)=

=3(3x+1){(x+1)}^2(5x+1)

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