What is the derivative of 1/((1+e^u)) ?

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

What is the first derivative of 1/((1+e^u)) ?

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

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derivative of

\frac{1}{( 1 + e ^{u} )}

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

Solution steps

\frac{d}{d u} (\frac{1}{1 + e ^{u}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

ln ((1 + 3 x)^{2})

3 t + 4

3 t - 1

\frac{3}{x ^{2} + 2}

\frac{d}{d z} (z^{3} + i)

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