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

Kye 2021-05-03 Answered
Find derivatives for the functions. Assume a, b, c, and k are constants.
$$\displaystyle{f{{\left({z}\right)}}}={\frac{{{z}^{{{2}}}+{1}}}{{{3}{z}}}}$$

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## Expert Answer

SchepperJ
Answered 2021-05-04 Author has 17469 answers
Simplify f(z)
$$\displaystyle{f{{\left({z}\right)}}}={\frac{{{z}^{{{2}}}+{1}}}{{{3}{z}}}}={\frac{{{1}}}{{{3}}}}{\left({z}+{z}^{{-{1}}}\right)}$$
Use the power rule tog et
$$\displaystyle{f}'{\left({z}\right)}={\frac{{{1}}}{{{3}}}}{\left({1}-{z}^{{-{2}}}\right)}={\frac{{{z}^{{{2}}}-{1}}}{{{3}{z}^{{{2}}}}}}$$

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