Given
[tex]x^2(x+1)^^3[/tex]
Find
Differentiation of the function
Explanation
[tex]\begin{gathered} f(x)=x^2(x+1^)^3 \\ f^{\prime}(x)=\frac{d(x^2)}{dx}.(x+1)^3+x^2.\frac{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}[/tex]
Final Answer
[tex]f^{\prime}(x)=x(x+1)^2(5x+2)[/tex]
