I have a problem as follows:

Let X have the pdf f(x)= θ * e^{( - θ x)}, 0 < x < infinity

find the pdf of Y = e^{x}

I've gone about this the way I normally do for these problems.

I have

G(y) = P(X < ln y) = integral of θ * e^{( - θ x)}dx from 0 to ln y = 1 - y^{-}^{θ}^{ }

So then I need g(y) = G'(y) of Y? which would be

θ * e^{( - θ (ln y)}??

or am I missing something super-duper obvious?

Thanks