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The power of a product is equal to the product of it's factors raised to the same power
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$\frac{d}{dx}\left(\frac{5}{8x^3}+2\cos\left(x\right)\right)$
Learn how to solve problems step by step online. Find the derivative d/dx(5/((2x)^3)+2cos(x)) using the sum rule. The power of a product is equal to the product of it's factors raised to the same power. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (2) is equal to the constant times the derivative of the function. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x).