Question

Differentiation of y =(x+1)^2(x^2+2x)

Answer 1

$\huge \pink{ \mathfrak{solution}}$

To Differentiate:

$y \: = ( {x + 1)}^{2} ( {x}^{2} + 2x)$

First solve Y

$\implies \: y = ( {x + 1)}^{2} ( {x}^{2} + 2x) \\ \\ \implies \: y = ( {x}^{2} + 1 + 2x)( {x}^{2} + 2x) \\ \\ \implies \: y = {x}^{4} + 2 {x}^{3} + {x}^{2} + 2x + 2 {x}^{3} + 4 {x}^{2} \\ \\ \implies \: y = {x}^{4} + 4 {x}^{3} + 5 {x}^{2} + 2x$

Now Differentiate w.r.t X

$\implies \: \frac{dy}{dx} = \frac{d}{dx} ( {x}^{4} + 4 {x}^{3} + 5 {x}^{2} + 2x) \\ \\ \implies \: \frac{dy}{dx} = 4 {x}^{4 - 1} + 4(3) {x}^{3 - 1} + 5(2) {x}^{2 - 1} + 2 {x}^{1 - 1} \\ \\ \implies \: \frac{dy}{dx} = 4 {x}^{3} + 12 {x}^{2} + 10x + 2$

Formula used:

$\star \boxed{ \bold{ \red{ \frac{d}{dx} {x}^{n} = n {x}^{n - 1} }}}$

Answer 2

Explanation:

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