Math Help - help with derivative

1. help with derivative

I need help with the following expression:

$d/dz (z^2+3i)$

Thank you.

2. Well just break it up:

$d/dz(z^2) + d/dz(3i)$
$= 2z + 0$
$= 2z$

In this case 3i is a constant, so the derivative is 0.

3. Thank you!!!
What if it were a bit more complicated?
For example,

$\frac{(z-3i)^2}{(z^2+4)^2}$?

4. Originally Posted by georgel
Thank you!!!
What if it were a bit more complicated?
For example,

$\frac{(z-3i)^2}{(z^2+4)^2}$?
I do not really know.
I know you can always use the definition, i.e. $f'(z)= \lim _{h \to 0} \frac{f(z+h)-f(z)}{h}$ where $f(z)=\frac{(z-3i)^2}{(z^2+4)^2}$. Of course $h\in \mathbb{C}$.

5. $\frac{(z-3i)^2}{(z^2+4)^2}$

If it were something like this, then you can rewrite it as so:

$(z-3i)^2(z^2+4)^{-2}$

From here you apply the product rule. (You'll have a chain rule to apply as well.)