Question

Find derivatives for the functions. Assume a, b, c, and k are constants. f(x)=\frac{x}{x+lnx}

Derivatives
ANSWERED
asked 2021-06-28
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}}}{{{x}+{\ln{{x}}}}}}\)

Answers (1)

2021-06-29
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}}}{{{x}+{\ln{{x}}}}}}\)
\(\displaystyle{j}'{\left({x}\right)}={\left({\frac{{{x}}}{{{1}+{\ln{{x}}}}}}\right)}'={\frac{{{\left({x}\right)}'{\left({1}+{\ln{{x}}}\right)}-{x}{\left({1}+{\ln{{x}}}\right)}'}}{{{\left({l}+{\ln{{x}}}\right)}^{{{2}}}}}}={\frac{{{1}+{\ln{{x}}}-{1}}}{{{\left({1}+{\ln{{x}}}\right)}^{{{2}}}={\frac{{{\ln{{x}}}}}{{{\left({1}+{\ln{{x}}}\right)}^{{{2}}}}}}}}}\)
\(\displaystyle{f}'{\left({x}\right)}={\frac{{{\ln{{x}}}}}{{{\left({1}+{\ln{{x}}}\right)}^{{{2}}}}}}\)
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