Question

Hi I need help differentiating question 1 f please, Thanks

Answer 1

Given

Find

Differentiation of the function

Step-by-step explanation

`\begin{gathered} f(x)=x^2(x+1^)^3 \\ f^(\prime)(x)=(d(x^2))/(dx).(x+1)^3+x^2.(d(x+1)^3)/(dx) \\ =2x(x+1)^3+3x^2(x+1)^2 \\ =x(x+1)^2[2(x+1)+3x] \\ =x(x+1)^2(2x+2+3x) \\ =x(x+1)^2(5x+2) \\ \\ \\ \end{gathered}`

Final Answer

`f^(\prime)(x)=x(x+1)^2(5x+2)`