# Solve for: y=(2x-x^2) * (x^3+4x^2)

## Expression: $y=\left( 2x-{x}^{2} \right) \times \left( {x}^{3}+4{x}^{2} \right)$

Take the derivative of both sides

$y '=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( \left( 2x-{x}^{2} \right) \times \left( {x}^{3}+4{x}^{2} \right) \right)$

Simplify the expression

$y '=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( 2{x}^{4}+8{x}^{3}-{x}^{5}-4{x}^{4} \right)$

Collect like terms

$y '=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( -2{x}^{4}+8{x}^{3}-{x}^{5} \right)$

Use differentiation rule $\frac{ \mathrm{d} }{ \mathrm{d}x} \left( f+g \right)=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( f \right)+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( g \right)$

$y '=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( -2{x}^{4} \right)+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( 8{x}^{3} \right)-\frac{ \mathrm{d} }{ \mathrm{d}x} \left( {x}^{5} \right)$

Find the derivative

$y '=-2 \times 4{x}^{3}+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( 8{x}^{3} \right)-\frac{ \mathrm{d} }{ \mathrm{d}x} \left( {x}^{5} \right)$

Find the derivative

$y '=-2 \times 4{x}^{3}+8 \times 3{x}^{2}-\frac{ \mathrm{d} }{ \mathrm{d}x} \left( {x}^{5} \right)$

Find the derivative

$y '=-2 \times 4{x}^{3}+8 \times 3{x}^{2}-5{x}^{4}$

Simplify the expression

$y '=-5{x}^{4}-8{x}^{3}+24{x}^{2}$

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