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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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$\frac{d}{dx}\left(\frac{1}{x}\right)+\frac{d}{dx}\left(-3\sin\left(x\right)\right)$
Learn how to solve problems step by step online. Find the derivative d/dx(1/x-3sin(x)) 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=-3 and g=\sin\left(x\right). The derivative of the constant function (-3) is equal to zero. Any expression multiplied by 0 is equal to 0.