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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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$\frac{d}{dx}\left(8\sqrt{x}\right)+\frac{d}{dx}\left(\frac{7}{x^5}\right)$
Learn how to solve problems step by step online. Find the derivative d/dx(8x^1/2+7/(x^5)) 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=8 and g=\sqrt{x}. The derivative of the constant function (8) is equal to zero. Any expression multiplied by 0 is equal to 0.