What is the derivative of 2/(1+e^x) ?

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

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

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

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Popular >

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

= 2 \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}

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

Simplify

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

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

n = 0 \sum \infty \frac{n + 1}{n}

\int sec^{4} (\frac{t}{2}) d t

\int x^{2} (x - 1)^{2} d x

\frac{2}{( 3 x + 1 )}, x = 2

\int \frac{1}{- x ^{2} + 8 x - 15} d x

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