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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

dy/dx=(dy/du)(du/dx)=-sin(u)×3=-3sin(3x).

We apply the same rule for sin(4x).

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