Question

what is the derivative with respect to time of: x*e^[i(w*t-a)]

Answer 1

let u=i(wt-a)
y=xe^u
find du/dt then dy/du

Answer 2

If I write the formula as a function f of t, I get:\[f(t)=x e^{i(wt-a)}\]
Is the number i in the formula meant as sqrt(-1)?
That would make it a complex-valued function.
It doesn't matter much, though.
We consider all other numbers than t as constants.

Also, the derivative of the exponential function e^t is e^t itself.
So differentiating your function wouldn't change it much, only use the following rules to get the answer:

1. (e^t)' = e^t (it is an exponential function)
2. (c*f(t))' = c*f'(t) (the x returns in the derivative unchanged)
3. Chain Rule (you need it for the exponent)

Answer 3

thank you!

Answer 4

you're welcome!