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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=4\sqrt{x}+\frac{1}{x}$ and $g=2x+\frac{-6}{\sqrt[3]{x}}$
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$\frac{d}{dx}\left(4\sqrt{x}+\frac{1}{x}\right)\left(2x+\frac{-6}{\sqrt[3]{x}}\right)+\left(4\sqrt{x}+\frac{1}{x}\right)\frac{d}{dx}\left(2x+\frac{-6}{\sqrt[3]{x}}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (4x^1/2+1/x)(2x+-6/(x^1/3)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=4\sqrt{x}+\frac{1}{x} and g=2x+\frac{-6}{\sqrt[3]{x}}. 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 linear function times a constant, is equal to the constant.