- #1
pellman
- 684
- 5
If z is complex, the following rules are true, right?
[tex]\frac{d}{dz}z^n = nz^{n-1}[/tex]
[tex]\frac{d}{dz}\ln{g(z)} = \frac{1}{g(z)} \frac{d}{dz}g(z)[/tex]
[tex] \frac{d}{dz}e^{g(z)}=e^{g(z)}\frac{d}{dz}g(z)[/tex]
These are of course the same rules as for real variables.
When do I need to be careful about taking derivatives with respect to complex variables?
Do all of the same rules apply as with real variables? Or do some rules fail?
[tex]\frac{d}{dz}z^n = nz^{n-1}[/tex]
[tex]\frac{d}{dz}\ln{g(z)} = \frac{1}{g(z)} \frac{d}{dz}g(z)[/tex]
[tex] \frac{d}{dz}e^{g(z)}=e^{g(z)}\frac{d}{dz}g(z)[/tex]
These are of course the same rules as for real variables.
When do I need to be careful about taking derivatives with respect to complex variables?
Do all of the same rules apply as with real variables? Or do some rules fail?