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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(\sqrt[3]{8xy}\right)\sqrt[3]{2y^2}+\sqrt[3]{8xy}\frac{d}{dx}\left(\sqrt[3]{2y^2}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (8xy)^1/3(2y^2)^1/3. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. 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 derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.