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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=
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$\frac{d}{dx}\left(x^3+6\right)\left(x^3-8\right)+\left(x^3+6\right)\frac{d}{dx}\left(x^3-8\right)$
Learn how to solve problems step by step online. Find the derivative using the quotient rule (x^3+6)(x^3-8). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. 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. The derivative of the constant function (6) is equal to zero.