Question

Dada a função f(z)=1/z, com z ≠​​​​​​​ 0. Qual o valor de f′(z)?

A. $\frac{1}{z^{2} }$

B. z²

C. -z²

D. ​​​$\frac{-1}{z^{2} }$

E. 2z²

Answer 1

$\displaystyle \sf f(z)=\frac{1}{z} \to f(z)=z^{-1} \\\\ derivando :\\\\ f'(z)=-1.z^{-1-1} \\\\ f'(z)=-1.z^{-2} \\\\ \boxed{\sf f'(z)=\frac{-1}{z^2}}\checkmark$

D