# Find derivatives for the functions. Assume a, b, c, and k are constants. f(z)=\frac{z^{2}+1}{3z}

Derivatives
Find derivatives for the functions. Assume a, b, c, and k are constants.
$$\displaystyle{f{{\left({z}\right)}}}={\frac{{{z}^{{{2}}}+{1}}}{{{3}{z}}}}$$

$$\displaystyle{f{{\left({z}\right)}}}={\frac{{{z}^{{{2}}}+{1}}}{{{3}{z}}}}={\frac{{{1}}}{{{3}}}}{\left({z}+{z}^{{-{1}}}\right)}$$
$$\displaystyle{f}'{\left({z}\right)}={\frac{{{1}}}{{{3}}}}{\left({1}-{z}^{{-{2}}}\right)}={\frac{{{z}^{{{2}}}-{1}}}{{{3}{z}^{{{2}}}}}}$$