Answer
$f'\left( x \right) = 3\cos x + 2\sin x$
Work Step by Step
$$\eqalign{
& f\left( x \right) = 3\sin x - 2\cos x \cr
& {\text{Differentiating}} \cr
& f'\left( x \right) = \frac{d}{{dx}}\left[ {3\sin x - 2\cos x} \right] \cr
& {\text{Use the difference rule for derivatives }} \cr
& f'\left( x \right) = \frac{d}{{dx}}\left[ {3\sin x} \right] - \frac{d}{{dx}}\left[ {2\cos x} \right] \cr
& {\text{Pull out the constants}} \cr
& f'\left( x \right) = 3\frac{d}{{dx}}\left[ {\sin x} \right] - 2\frac{d}{{dx}}\left[ {\cos x} \right] \cr
& {\text{Use the Derivatives of Trigonometric Functions }} \cr
& f'\left( x \right) = 3\left( {\cos x} \right) - 2\left( { - \sin x} \right) \cr
& {\text{Simplify}} \cr
& f'\left( x \right) = 3\cos x + 2\sin x \cr} $$
