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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x^2-4$ and $g=\left(x+1\right)^2\left(x+3\right)\left(x-5\right)$
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$\frac{d}{dx}\left(x^2-4\right)\left(x+1\right)^2\left(x+3\right)\left(x-5\right)+\left(x^2-4\right)\frac{d}{dx}\left(\left(x+1\right)^2\left(x+3\right)\left(x-5\right)\right)$
Learn how to solve problems step by step online. Find the derivative of (x^2-4)(x+1)^2(x+3)(x-5). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^2-4 and g=\left(x+1\right)^2\left(x+3\right)\left(x-5\right). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\left(x+1\right)^2 and g=\left(x+3\right)\left(x-5\right). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x+3 and g=x-5. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.