Final Answer
Step-by-step Solution
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$
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$\frac{d}{dx}\left(\left(x^2+1\right)^2\right)\left(x-1\right)^5x^4+\left(x^2+1\right)^2\left(\frac{d}{dx}\left(\left(x-1\right)^5\right)x^4+\left(x-1\right)^5\frac{d}{dx}\left(x^4\right)\right)$
Learn how to solve problems step by step online. Find the derivative using the quotient rule d/dx((x^2+1)^2(x-1)^5x^4). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. 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 power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.