The derivative of a complex function. 
Question:
Find all points at which the complex valued function $f$ define by $$f(z)=(2+i)z^3-iz^2+4z-(1+7i)$$ has a derivative.

I know that $z^3$,$z^2$, and $z$ are differentiable everywhere in the domain of $f$, but how can I write my answer formally? Please can somebody help?
Note:I want to solve the problem without using Cauchy-Riemann equations.

I'm not sure where the question is coming from (what you know/can know/etc.).
But some things that you might use: you might just give the derivative, if you know how to take it. Perhaps you might verify it with the Cauchy-Riemann equations. Alternatively, differentiation is linear (which you might prove, if you haven't), and finite linear combination of differentiable functions is also differentiable. Or you know the series expansion, it's finite, and converges in infinite radius - thus it's holomorphic.
But any of these would lead to a complete solution. Does that make sense?
