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Popular >

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

Solution

\frac{d}{d x} (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

(\partial)/(\partial x)(ln((cos(x)y)^z))

\frac{\partial}{\partial x} (ln ((cos (x) y)^{z}))

limit as x approaches 3 of sqrt(3x+7)

x \to 3 lim (3 x + 7)

integral from 0 to 2pi of cos(t)

\int_{0}^{2 π} cos (t) d t

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

x \to 5 lim (5 - x)

limit as x approaches-infinity of 2/x

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

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)