What is the derivative of 1/(1+e^{0.5x}) ?

The derivative of 1/(1+e^{0.5x}) is -(0.5e^{0.5x})/((1+e^{0.5x))^2}

What is the first derivative of 1/(1+e^{0.5x}) ?

The first derivative of 1/(1+e^{0.5x}) is -(0.5e^{0.5x})/((1+e^{0.5x))^2}

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\frac{d}{d x} (\frac{1}{1 + e ^{0.5 x}})

- \frac{0.5 e ^{0.5 x}}{( 1 + e ^{0.5 x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{1 + e ^{0.5 x}})

Apply exponent rule:

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

= \frac{d}{d x} ((1 + e^{0.5 x})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + e ^{0.5 x} ) ^{2}} \frac{d}{d x} (1 + e^{0.5 x})

= - \frac{1}{( 1 + e ^{0.5 x} ) ^{2}} \frac{d}{d x} (1 + e^{0.5 x})

\frac{d}{d x} (1 + e^{0.5 x}) = 0.5 e^{0.5 x}

= - \frac{1}{( 1 + e ^{0.5 x} ) ^{2}} \cdot 0.5 e^{0.5 x}

Simplify

- \frac{1}{( 1 + e ^{0.5 x} ) ^{2}} \cdot 0.5 e^{0.5 x} : - \frac{0.5 e ^{0.5 x}}{( 1 + e ^{0.5 x} ) ^{2}}

= - \frac{0.5 e ^{0.5 x}}{( 1 + e ^{0.5 x} ) ^{2}}

n = 1 \sum \infty n e^{- 6 n}

\frac{d ^{2}}{d z ^{2}} (z^{2} e^{z})

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

\frac{d ^{2}}{d x ^{2}} (6 x^{2} + 5 x)

(t + 1) d t - \frac{1}{y ^{2}} d y = 0

What is the derivative of 1/(1+e^{0.5x}) ?
The derivative of 1/(1+e^{0.5x}) is -(0.5e^{0.5x})/((1+e^{0.5x))^2}
What is the first derivative of 1/(1+e^{0.5x}) ?
The first derivative of 1/(1+e^{0.5x}) is -(0.5e^{0.5x})/((1+e^{0.5x))^2}