Find the derivative $\frac{d}{dx}\left(\sin\left(x\right)+x\cos\left(x\right)\right)$ using the sum rule

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$\frac{d}{dx}\left(\sin\left(x\right)\right)+\frac{d}{dx}\left(x\cos\left(x\right)\right)$

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative (d/dx)(sin(x)+cos(x)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=\cos\left(x\right) and g=x. The derivative of the linear function is equal to 1. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}.