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