Examine what is f(x) if primitive of function is sin 3x-cos4x?
You need to use the equation that relates a primitive and its function, such that:
`F'(x) = f(x) or int f(x)dx = F(x) + c`
`F(x)` represents the primitive
Since the problem provides the equation of primitive `F(x) = sin 3x - cos 4x` , you need to differentiate the primitive with respect to x, using the chain rule, such that:
`F'(x) = (sin 3x - cos 4x)' => F'(x) = (cos 3x)*(3x)' - (-sin 4x)*(4x)'`
`F'(x) = 3cos 3x + 4sin 4x => f(x) = 3cos 3x + 4sin 4x`
Hence, evaluating the function `f(x)` , differentiating the given primitive, yields `f(x) = 3cos 3x + 4sin 4x` .