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The derivative of a sum of two or more functions is the sum of the derivatives of each function
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$\frac{d}{dx}\left(12x^5\right)+\frac{d}{dx}\left(-4x^{-4}\right)+\frac{d}{dx}\left(\frac{3}{2\sqrt[3]{x^{2}}}\right)$
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(12x^5-4x^(-4)3/(2x^2/3)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=12 and g=x^5. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=-4 and g=x^{-4}. The derivative of the constant function (12) is equal to zero.