What is the derivative of ln((1+e^x/(1-e^x))) ?

The derivative of ln((1+e^x/(1-e^x))) is (2e^x)/((e^x+1)(-e^x+1))

What is the first derivative of ln((1+e^x/(1-e^x))) ?

The first derivative of ln((1+e^x/(1-e^x))) is (2e^x)/((e^x+1)(-e^x+1))

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Popular >

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

\frac{2 e ^{x}}{( e ^{x} + 1 ) ( - e ^{x} + 1 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{1 + e ^{x}}{1 - e ^{x}}) = \frac{2 e ^{x}}{( 1 - e ^{x} ) ^{2}}

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

Simplify

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

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

\int (x - 1)^{3} d x

\int \frac{1}{( x + 1 ) ^{3}} d x

x \to 2 lim (4 - x^{2})

x \to 2 lim (5 x^{4})

x \to 2 lim (\frac{x - 2}{x + 2})

What is the derivative of ln((1+e^x/(1-e^x))) ?
The derivative of ln((1+e^x/(1-e^x))) is (2e^x)/((e^x+1)(-e^x+1))
What is the first derivative of ln((1+e^x/(1-e^x))) ?
The first derivative of ln((1+e^x/(1-e^x))) is (2e^x)/((e^x+1)(-e^x+1))