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Learn how to solve differential calculus problems step by step online. Find the derivative of (2/(x^1/2)-3^1/2)(4xx^1/3+(x^2^1/3)/(3x)). Simplifying. Simplifying. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\frac{2}{\sqrt{x}}-\sqrt{3} and g=4\sqrt{x}}.
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The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.