Question

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

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

Answers (1)

2021-05-04
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
\(\displaystyle{f}'{\left({z}\right)}={\frac{{{1}}}{{{3}}}}{\left({1}-{z}^{{-{2}}}\right)}={\frac{{{z}^{{{2}}}-{1}}}{{{3}{z}^{{{2}}}}}}\)
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-06-08
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{f{{\left({z}\right)}}}={\frac{{{z}^{{{2}}}+{1}}}{{\sqrt{{{z}}}}}}\)
asked 2021-06-12
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}^{{{2}}}}}}+{5}\sqrt{{{x}}}-{7}\)
asked 2021-06-24
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{f{{\left({x}\right)}}}={5}{x}^{{{4}}}+{\frac{{{1}}}{{{x}^{{{2}}}}}}\)
asked 2021-05-08
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}+{3}{x}+{2}}}{{{x}+{1}}}}\)
asked 2021-06-18
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{a}^{{{2}}}-{x}^{{{2}}}}}{{{a}^{{{2}}}+{x}^{{{2}}}}}}\)
asked 2021-06-13
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}^{{{3}}}}}{{{9}}}}{\left({3}{\ln{{x}}}-{1}\right)}\)
asked 2021-05-11
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{f{{\left({t}\right)}}}={2}{t}{e}^{{{t}}}-{\frac{{{1}}}{{\sqrt{{{t}}}}}}\)
asked 2021-05-09
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{g{{\left({x}\right)}}}=−{\frac{{{1}}}{{{2}}}}{\left({x}^{{{5}}}+{2}{x}−{9}\right)}\)
asked 2021-05-05
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{y}={\frac{{{e}^{{{2}{x}}}}}{{{x}^{{{2}}}+{1}}}}\)
asked 2021-06-20
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{h}{\left({r}\right)}={\frac{{{r}^{{{2}}}}}{{{2}{r}+{1}}}}\)
...