Find the derivative of y(x)=x3(x+1)2 with respect to x.
A
3x2(x+1)2−2x3(x+1)3
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B
3x(x+1)2−2x3(x+1)3
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C
3x2(x+1)2−x(x+1)3
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D
3x2(x+1)−2x3(x+1)2
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Solution
The correct option is A3x2(x+1)2−2x3(x+1)3 We can rewrite this function as y(x)=x3(x+1)−2
Apply product rule, dydx=(x+1)−2d(x3)dx+x3d(x+1)−2dx dydx=(x+1)−23x2+x3(−2)(x+1)−3 dydx=3x2(x+1)2−2x3(x+1)3