What is the derivative of ln((5+e^x/(5-e^x))) ?

The derivative of ln((5+e^x/(5-e^x))) is (10e^x)/((e^x+5)(-e^x+5))

What is the first derivative of ln((5+e^x/(5-e^x))) ?

The first derivative of ln((5+e^x/(5-e^x))) is (10e^x)/((e^x+5)(-e^x+5))

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Popular >

\frac{d}{d x} (ln (\frac{5 + e ^{x}}{5 - e ^{x}}))

\frac{10 e ^{x}}{( e ^{x} + 5 ) ( - e ^{x} + 5 )}

Solution steps

\frac{d}{d x} (ln (\frac{5 + e ^{x}}{5 - e ^{x}}))

Apply the chain rule:

\frac{1}{\frac{5 + e ^{x}}{5 - e ^{x}}} \frac{d}{d x} (\frac{5 + e ^{x}}{5 - e ^{x}})

= \frac{1}{\frac{5 + e ^{x}}{5 - e ^{x}}} \frac{d}{d x} (\frac{5 + e ^{x}}{5 - e ^{x}})

\frac{d}{d x} (\frac{5 + e ^{x}}{5 - e ^{x}}) = \frac{10 e ^{x}}{( 5 - e ^{x} ) ^{2}}

= \frac{1}{\frac{5 + e ^{x}}{5 - e ^{x}}} \cdot \frac{10 e ^{x}}{( 5 - e ^{x} ) ^{2}}

Simplify

\frac{1}{\frac{5 + e ^{x}}{5 - e ^{x}}} \cdot \frac{10 e ^{x}}{( 5 - e ^{x} ) ^{2}} : \frac{10 e ^{x}}{( e ^{x} + 5 ) ( - e ^{x} + 5 )}

= \frac{10 e ^{x}}{( e ^{x} + 5 ) ( - e ^{x} + 5 )}

x \to \infty lim (\frac{arctan ( x )}{\frac{1}{x} - 4})

\frac{d}{d x} (- \frac{x ^{7}}{7} + \frac{x ^{5}}{5})

y = \frac{3 x - 2}{2 x + 1}

\frac{\partial}{\partial x} (\frac{2 y}{( x + y ) ^{2}})

\int \frac{x ^{3}}{( x ^{2} + a ^{2} ) ^{3}} d x

What is the derivative of ln((5+e^x/(5-e^x))) ?
The derivative of ln((5+e^x/(5-e^x))) is (10e^x)/((e^x+5)(-e^x+5))
What is the first derivative of ln((5+e^x/(5-e^x))) ?
The first derivative of ln((5+e^x/(5-e^x))) is (10e^x)/((e^x+5)(-e^x+5))