Final Answer
Step-by-step Solution
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\left(2-x\right)^3$ and $g=\left(1-x^2\right)^2$
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$\frac{d}{dx}\left(\left(2-x\right)^3\right)\left(1-x^2\right)^2+\left(2-x\right)^3\frac{d}{dx}\left(\left(1-x^2\right)^2\right)$
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}. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of a sum of two or more functions is the sum of the derivatives of each function.