I am working on a problem, and I have the solution, but there is a step that I'm having difficulty understanding.Given: Current in a 50 micro Henry inductor is iL18te^(-10t) amps, for t 0Find the voltage across the inductor.Here's the steps that are shown.VL(t) L(d/dt) * i(t)VL(t) [50*10^(-6) d/dt] * 18te^(-10t)VL(t) (9/10000)e^(-10t) - (9/1000)te^(-10t)What I don't understand is this last step. How do you get 9/10000 and 9/1000? Could someone please explain this?
The 9/10000 is just another way of writing 50e-6 x 18 x 10 in the first term and 50e-6 x 18 in the second term. Do you understand that you are differentiating t x e^(-10t) and that you apply the chain rule? You get 10 e^(-10t) + te^(-10t). Each of these terms is multiplied by the constant 50e-6 x 18.
You need to learn how to differentiate.
