What is the derivative of (14/((1+e^{-x))}) ?

The derivative of (14/((1+e^{-x))}) is (14e^{-x})/((1+e^{-x))^2}

What is the first derivative of (14/((1+e^{-x))}) ?

The first derivative of (14/((1+e^{-x))}) is (14e^{-x})/((1+e^{-x))^2}

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\frac{d}{d x} (\frac{14}{( 1 + e ^{- x} )})

\frac{14 e ^{- x}}{( 1 + e ^{- x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{14}{( 1 + e ^{- x} )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 14 \frac{d}{d x} (\frac{1}{1 + e ^{- x}})

Apply exponent rule:

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

= 14 \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}

= 14 (- \frac{1}{( 1 + e ^{- x} ) ^{2}} (- e^{- x}))

Simplify

14 (- \frac{1}{( 1 + e ^{- x} ) ^{2}} (- e^{- x})) : \frac{14 e ^{- x}}{( 1 + e ^{- x} ) ^{2}}

= \frac{14 e ^{- x}}{( 1 + e ^{- x} ) ^{2}}

n = 2 \sum \infty \frac{2}{n ^{2} - 1}

\frac{d y}{d x} = 3 - y

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

f (x) = - \frac{8}{x}

x \to 3 lim (- 2 (x - 2)^{2} + 4)

What is the derivative of (14/((1+e^{-x))}) ?
The derivative of (14/((1+e^{-x))}) is (14e^{-x})/((1+e^{-x))^2}
What is the first derivative of (14/((1+e^{-x))}) ?
The first derivative of (14/((1+e^{-x))}) is (14e^{-x})/((1+e^{-x))^2}