Complex derivatives

If i had been a real number, what would the first and second derivatives have been then?

 

EXACTLY!
And that is precisely what holds when "i" is a complex/imaginary number as well!

 

When dealing with these things, forget i is anything, just remember its a constant. Then after the actual differentiation, you can remember what it is.

 

Yeah. If

[tex]\exp(ix),\,\,\,x\in \mathbb{R},[/tex]

(which is what it looks like you have) then it's what the above two said. But if you have

[tex]\exp(iz),\,\,\,z\in \mathbb{Z},[/tex]

you need to be more careful. Let us know if that is indeed what you have.

 

what are you doing in a de course ifm you do not know the derivative of e^z?

 

I'm doing the same derivative problem & i was wondering if you could give any tips on how to solve the derivative of e^ix? I would really appreciate it. A good reference website, anything assistance at all.

 

That is exactly what has been answered in each of these responses. For any constant, a, the derivative of [itex]e^{ax}[/itex] is [itex]ae^{ax}[/itex].

That is a result of the very basic fact that the derivative of [itex]e^x[/itex] is [itex]e^x[/itex] (world's easiest derivative!) and the chain rule.

 

[tex]\frac{d}{dx}(e^{jx})=je^{jx}[/tex]
[tex]\frac{d^2}{dx^2}(e^{jx})=-e^{jx}[/tex]

 

Actually I myself was once in an ode course when I had forgot the derivative of e^x. My solution was to go get a Schaum's outline series of ode and do a lot of problems and review my $$$ off.