## Derivative of an imaginary number

I was just wondering if anyone knows the rule when taking the derivative of an imaginary number(i). For example: d(ix)/dx=?

Thanks:)

 PhysOrg.com science news on PhysOrg.com >> Heat-related deaths in Manhattan projected to rise>> Dire outlook despite global warming 'pause': study>> Sea level influenced tropical climate during the last ice age
 Recognitions: Science Advisor For the purposes of differential calculus, i is simply another constant. Therefore d(ix)/dx=idx/dx=i
 Recognitions: Gold Member Science Advisor Staff Emeritus You don't take the derivative of "numbers" in general. You take the derivative of functions. Of course you can treat any number, including complex numbers, as a "constant function". As "mathman" said (and he ought to know!) d(ix)/dx= i just as d(ax)/dx= a for any number a. If you allow the variable, x, to be a complex number, then it becomes more interesting!

## Derivative of an imaginary number

how can i proof if this function has a derivative?

1/[ z*sin(z)*g(z)] from first principle?

z= x + jy.

 Recognitions: Gold Member Science Advisor Staff Emeritus You don't- not with information on g. And, whatever g is, that function is certainly NOT differentiable where it is not defined: any multiple of $\pi$.
 suppose to be 1/[ z*sin(z)*cos (z)]