# Derivative in the complex plane

1. Feb 22, 2017

### cragar

1. The problem statement, all variables and given/known data
$f(z)=2x^3+3iy^2$ then it wants
$f '(x+ix^2)$
3. The attempt at a solution

So I take the partial with respect to x and i get
$6x^2$ then partial with respect to y and I get
6iy, then I plug in x for the real part and x-squared for the imaginary part,
then I get $f ' (x+ix^2)=6x^2+6ix^2$
the back of my book has $f' = 6x^2$
I dont see why its not what I got.

Last edited by a moderator: Feb 22, 2017
2. Feb 22, 2017

### Staff: Mentor

What do you know about complex differentiation? How is it defined? Which formulas do you know?
If you took the partial differentials, then this is not the complex differential. So why did you use them, i.e. how are they related?

3. Feb 22, 2017

### cragar

I know cauchy reimann formulas, so I did it wrong, first off it doesn't satisfy c-r formulas,
but for the imaginary part I should of taken the partial with respect to x as cauchy reimann implies, then that partial would be zero,
then the derivative would be 6x^2 .