Derivatives of Exponential, Logarithmic and Trigonometric Functions

Let \(f(x) = \mathrm{e}^{-3x}\) and \(g(x) = \sin{ \left(x - \frac{\pi}{3} \right)} \).

1. Write down
   1. \(f'(x)\);
   2. \(g(x)\).[2]
2. Let \(h(x) = \mathrm{e}^{-3x} \sin{ \left(x - \frac{\pi}{3} \right)} \). Find the exact value of \(h' \left(\frac{\pi}{3} \right)\).[4]