I have looked the similar questions but all the questions are hard one and I can't understand.
My question is find the derivative $\dfrac{4z+z^3-z^4} {z^2}$, $z \neq 0$.
I got this answer:
however answer is $\dfrac{-2z^3+z^2-4}{z^2}$, looks easy; however, I can't get the answer.
Can you please explain it in step by step? I appreciate it. thanks alot.

  • $\begingroup$ Have you learned the quotient rule for derivatives? The derivative of $\dfrac{f(z)}{g(z)}$ is? $\endgroup$ – user23784 Apr 7 '12 at 5:52
  • $\begingroup$ no! I havn't learn yet. $\endgroup$ – Cin Sb Sangpi Apr 7 '12 at 5:55
  • $\begingroup$ Ah. No worries, I think anon's answer should get you there without it. $\endgroup$ – user23784 Apr 7 '12 at 5:57
  • $\begingroup$ Maybe you should first compute the derivative of $z^n$? $\endgroup$ – copper.hat Apr 7 '12 at 7:34

It helps in this case to divide through for a simpler expression:


Now to differentiate:


If you want to put this over a denominator again:



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