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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$
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$\frac{d}{dx}\left(\sqrt{xy}\right)\sqrt[4]{2x^2y}\sqrt[5]{3x^3y^2}+\sqrt{xy}\left(\frac{d}{dx}\left(\sqrt[4]{2x^2y}\right)\sqrt[5]{3x^3y^2}+\sqrt[4]{2x^2y}\frac{d}{dx}\left(\sqrt[5]{3x^3y^2}\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (xy)^1/2(2x^2y)^1/4(3x^3y^2)^1/5. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. The power of a product is equal to the product of it's factors raised to the same power. The power of a product is equal to the product of it's factors raised to the same power. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.