## Step-by-step explanation

Problem to solve:

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

$\frac{d}{dx}\left(4\cos\left(3x\right)\right)+\frac{d}{dx}\left(-3\sin\left(4x\right)\right)$

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative (d/dx)(4cos(3*x)-3sin(4*x)) using the sum rule. The derivative of a sum of two functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (4) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant (-3) is equal to the constant times the derivative of the function. 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)}.