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Popular >

derivative of (1+e^{-x}^{-1})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of y=x^{2x+5}derivative of

y = x^{2 x + 5}

(\partial)/(\partial x)(ln(9-x^2-y^2))

\frac{\partial}{\partial x} (ln (9 - x^{2} - y^{2}))

(\partial)/(\partial z)(z(y-yz)^4)

\frac{\partial}{\partial z} (z (y - yz)^{4})

integral from 0 to 5 of e^{-x}

\int_{0}^{5} e^{- x} d x

(x^2+1)(dy)/(dx)+3x(y-1)=0,y(0)=3

(x^{2} + 1) \frac{d y}{d x} + 3 x (y - 1) = 0, y (0) = 3

Frequently Asked Questions (FAQ)

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