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Hi I need help differentiating question 1 f please, Thanks

Hi I Need Help Differentiating Question 1 F Please Thanks class=

Sagot :

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]

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