Exercise
Find the derivative of the following function:
f(x)={(3x-1)}^2\cdot{(x+1)}^3
Final Answer
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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