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 $f=x^2+3x$ and $g=\left(x-2\right)\left(x^2+1\right)$
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$\frac{d}{dx}\left(x^2+3x\right)\left(x-2\right)\left(x^2+1\right)+\left(x^2+3x\right)\frac{d}{dx}\left(\left(x-2\right)\left(x^2+1\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (x^2+3x)(x-2)(x^2+1). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^2+3x and g=\left(x-2\right)\left(x^2+1\right). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x-2 and g=x^2+1. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a sum of two or more functions is the sum of the derivatives of each function.