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** Step-by-step Solution **

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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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$\frac{d}{dx}\left(e^{2x}\right)+\frac{d}{dx}\left(-x\cos\left(xy\right)\right)$

Learn how to solve differential equations problems step by step online. Find the derivative d/dx(e^(2x)-xcos(xy)) using the sum rule. 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 (-1) is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\cos\left(xy\right). Simplify the product -(\frac{d}{dx}\left(x\right)\cos\left(xy\right)+x\frac{d}{dx}\left(\cos\left(xy\right)\right)).

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