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Popular >

derivative of ln((e^x)/(1+e^x))

Solution

derivative of

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

Solution

1 - \frac{e ^{x}}{1 + e ^{x}}

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d x}{d x} = 1

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

= 1 - \frac{e ^{x}}{1 + e ^{x}}

Popular Examples

simplify ln(sqrt((a^2-z^2)/(a^2+z^2)))simplify

ln (\frac{a ^{2} - z ^{2}}{a ^{2} + z ^{2}})

limit as x approaches 5 of (x-5)/(x-5)

x \to 5 lim (\frac{x - 5}{x - 5})

integral of 1/(4x^2-4x+5)

\int \frac{1}{4 x ^{2} - 4 x + 5} d x

(dy)/(dx)tan(y)= 1/x

\frac{d y}{d x} tan (y) = \frac{1}{x}

limit as x approaches 1 of 18x^{100}-5

x \to 1 lim (18 x^{100} - 5)

Frequently Asked Questions (FAQ)

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