What is the derivative of ln((7+e^x/(7-e^x))) ?

The derivative of ln((7+e^x/(7-e^x))) is (14e^x)/((e^x+7)(-e^x+7))

What is the first derivative of ln((7+e^x/(7-e^x))) ?

The first derivative of ln((7+e^x/(7-e^x))) is (14e^x)/((e^x+7)(-e^x+7))

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Popular >

\frac{d}{d x} (ln (\frac{7 + e ^{x}}{7 - e ^{x}}))

\frac{14 e ^{x}}{( e ^{x} + 7 ) ( - e ^{x} + 7 )}

Solution steps

\frac{d}{d x} (ln (\frac{7 + e ^{x}}{7 - e ^{x}}))

Apply the chain rule:

\frac{1}{\frac{7 + e ^{x}}{7 - e ^{x}}} \frac{d}{d x} (\frac{7 + e ^{x}}{7 - e ^{x}})

= \frac{1}{\frac{7 + e ^{x}}{7 - e ^{x}}} \frac{d}{d x} (\frac{7 + e ^{x}}{7 - e ^{x}})

\frac{d}{d x} (\frac{7 + e ^{x}}{7 - e ^{x}}) = \frac{14 e ^{x}}{( 7 - e ^{x} ) ^{2}}

= \frac{1}{\frac{7 + e ^{x}}{7 - e ^{x}}} \cdot \frac{14 e ^{x}}{( 7 - e ^{x} ) ^{2}}

Simplify

\frac{1}{\frac{7 + e ^{x}}{7 - e ^{x}}} \cdot \frac{14 e ^{x}}{( 7 - e ^{x} ) ^{2}} : \frac{14 e ^{x}}{( e ^{x} + 7 ) ( - e ^{x} + 7 )}

= \frac{14 e ^{x}}{( e ^{x} + 7 ) ( - e ^{x} + 7 )}

\int_{0}^{5} \frac{1}{x ^{\frac{13}{12}}} d x

\frac{d}{d x} (lo g_{n} (x))

t^{2} \frac{d y}{d t} + y^{2} = t y

\int x (1 - 2 x) d x

What is the derivative of ln((7+e^x/(7-e^x))) ?
The derivative of ln((7+e^x/(7-e^x))) is (14e^x)/((e^x+7)(-e^x+7))
What is the first derivative of ln((7+e^x/(7-e^x))) ?
The first derivative of ln((7+e^x/(7-e^x))) is (14e^x)/((e^x+7)(-e^x+7))