I have been given this problem to solve:
Define the function f(t) by $$ f(t) =\begin{cases} e^{-kt},& t \geq 0 \\ 0,& \text{otherwise}\end{cases} $$
where $k > 0$ is a real number.
Calculate the F.T. of df/dt in two ways: (i) by differentiating f(t) and then finding the F.T. of the result; and (ii) using the F.T. differentiation property.
I have managed to do part (i) and have come up with the answer of $\frac{jw}{jw+k}$.
I have come up with $F(w) = \frac{1}{k+jw}$ as the transform for f(t) but am struggling to complete part (ii) as I am unsure about the notation of the fourier differentiation property.
$$\frac{d(f(t))}{dt} \rightleftharpoons jwF(w)$$
Could someone explain the steps I need to take to solve part (ii), an explanation of the steps would suffice, I should then be able to finish the problem.
For future reference when differentiating something with a jump in it is important to add a delta dirac function
As for part (ii) it is a simple matter of multiplying the original transform by $jw$