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\frac{d}{dx}\left(\left(2-x\right)^3\left(1-x^2\right)^2\right)

Find the derivative of (2-1x)^3(1-1x^2)^2

Answer

$-3x^{6}+12x^{5}-24x^{3}+24x^2-3x^2+12x-12-4x^{3}\left(1-x^2\right)\left(2-x\right)+16x^2\left(1-x^2\right)\left(2-x\right)-16x\left(1-x^2\right)\left(2-x\right)-6x^{4}$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(\left(2-x\right)^3\left(1-x^2\right)^2\right)$
1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\left(2-x\right)^3$ and $g=\left(1-x^2\right)^2$

$\left(2-x\right)^3\frac{d}{dx}\left(\left(1-x^2\right)^2\right)+\left(1-x^2\right)^2\frac{d}{dx}\left(\left(2-x\right)^3\right)$

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Answer

$-3x^{6}+12x^{5}-24x^{3}+24x^2-3x^2+12x-12-4x^{3}\left(1-x^2\right)\left(2-x\right)+16x^2\left(1-x^2\right)\left(2-x\right)-16x\left(1-x^2\right)\left(2-x\right)-6x^{4}$
$\frac{d}{dx}\left(\left(2-x\right)^3\left(1-x^2\right)^2\right)$

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

~ 1.81 seconds