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 $f=\left(x^2+1\right)^3$ and $g=\left(x-1\right)^5x^3$
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$\frac{d}{dx}\left(\left(x^2+1\right)^3\right)\left(x-1\right)^5x^3+\left(x^2+1\right)^3\frac{d}{dx}\left(\left(x-1\right)^5x^3\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (x^2+1)^3(x-1)^5x^3. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\left(x^2+1\right)^3 and g=\left(x-1\right)^5x^3. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\left(x-1\right)^5 and g=x^3. 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}.