# Is the first principles?

• Apr 21st 2010, 03:38 AM
piglet
Is the first principles?
Im trying to prove function $
f:\mathbb{C}\longrightarrow\mathbb{C}$
defined by $f(z) = z^{2}+z$ is differentiable everywhere in $C$ using derivative as a limit

Is this asking me to use first principles to show this?

• Apr 21st 2010, 03:42 AM
undefined
Quote:

Originally Posted by piglet
Im trying to prove function $
f:\mathbb{C}\longrightarrow\mathbb{C}$
defined by $f(z) = z^{2}+z$ is differentiable everywhere in $C$ using derivative as a limit

Is this asking me to use first principles to show this?

It sounds like you're supposed to write the definition of derivative in terms of a limit, then plug in f(z), then show that the limit exists for all z in C.
• Apr 21st 2010, 04:41 AM
HallsofIvy
Yes, show that $\lim_{h\to 0}\frac{(z+ h)^2+ (z+h)- (z^2+ z)}{h}$ exists.