The derivative with respect to x is -12sin(3x)-12cos(4x). We get this as follows:
The derivative of a sum (or difference) is the sum (or difference) of the derivatives.
Derivative of cos(u) is -sin(u), then we apply the chain rule, putting u=3x, if we need the derivative of cos(3x):
If y=cos(3x)=cos(u), du/dx=3 and
We apply the same rule for sin(4x).