** Final Answer

**

** Step-by-step Solution **

Problem to solve:

** Specify the solving method

**

**

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.

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

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)}.

** Final Answer

**