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The derivative of a sum of two or more functions is the sum of the derivatives of each function

Learn how to solve sum rule of differentiation problems step by step online.

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

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dy(e^(2y)-ycos(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=y and g=\cos\left(xy\right). Simplify the product -(\frac{d}{dy}\left(y\right)\cos\left(xy\right)+y\frac{d}{dy}\left(\cos\left(xy\right)\right)).

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