Question

Find the derivative of the function f(x) = ln(e^x + 12)

Analyzing functions
ANSWERED
asked 2021-01-15
Find the derivative of the function \(\displaystyle{f{{\left({x}\right)}}}={\ln{{\left({e}^{{x}}+{12}\right)}}}\)

Answers (1)

2021-01-16
\(\displaystyle{f}{1}{\left({x}\right)}=\frac{{1}}{{{e}^{{x}}+{12}}}\times\frac{{d}}{{\left.{d}{x}\right.}}\times{\left({e}^{{x}}+{12}\right)}\)
\(\displaystyle=\frac{{1}}{{{e}^{{x}}+{12}}}\times{\left({e}^{{x}}+{0}\right)}=\frac{{e}^{{x}}}{{{e}^{{x}}+{12}}}\)
(Since \(\displaystyle\frac{{d}}{{\left.{d}{x}\right.}}{\left({\ln{{x}}}\right)}=\frac{{1}}{{x}}\)) and (\(\displaystyle{\sin{{c}}}{e}\frac{{d}}{{\left.{d}{x}\right.}}\)(constant) = 0, \(\displaystyle\frac{{d}}{{\left.{d}{x}\right.}}{\left({e}^{{x}}\right)}={e}^{{x}}\))
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