Step-by-step Solution

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Step-by-step explanation

Problem to solve:

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

Learn how to solve product rule of differentiation problems step by step online.

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

Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule (d/dx)((2-x)^3(1-x^2)^2). 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. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Subtract the values 3 and -1. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

$-3\left(2-x\right)^{2}\left(1-x^2\right)^2-4x\left(2-x\right)^3\left(1-x^2\right)$
$\frac{d}{dx}\left(\left(2-x\right)^3\left(1-x^2\right)^2\right)$