Nth Derivative of a interesting function

[ayae]

Hey guys, if the function f(x) has a special property that; f'(x) = f(x) g(x)

Whats the easiest way to find the nth derivative of f(x) in terms of f(x), g(x) and g'(x)'s derivatives?

The same problem rephrased is if q(x) is the logarithmic derivative of f(x), then what's the nth derivative of f(x) in terms of f(x) and derivatives of q(x)?

I've had limited success but it seems to be getting a little hairy and I pressume that there is a better method.

 

[micromass]

Maybe you can use that
$$f(x)=e^{\int{g(x)dx}}$$