What is the derivative of (40/(1+79e^{-x)}) ?

The derivative of (40/(1+79e^{-x)}) is (3160e^{-x})/((1+79e^{-x))^2}

What is the first derivative of (40/(1+79e^{-x)}) ?

The first derivative of (40/(1+79e^{-x)}) is (3160e^{-x})/((1+79e^{-x))^2}

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\frac{d}{d x} (\frac{40}{1 + 79 e ^{- x}})

\frac{3160 e ^{- x}}{( 1 + 79 e ^{- x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{40}{1 + 79 e ^{- x}})

Take the constant out:

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

= 40 \frac{d}{d x} (\frac{1}{1 + 79 e ^{- x}})

Apply exponent rule:

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

= 40 \frac{d}{d x} ((1 + 79 e^{- x})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + 79 e ^{- x} ) ^{2}} \frac{d}{d x} (1 + 79 e^{- x})

= - \frac{1}{( 1 + 79 e ^{- x} ) ^{2}} \frac{d}{d x} (1 + 79 e^{- x})

\frac{d}{d x} (1 + 79 e^{- x}) = - 79 e^{- x}

= 40 (- \frac{1}{( 1 + 79 e ^{- x} ) ^{2}} (- 79 e^{- x}))

Simplify

40 (- \frac{1}{( 1 + 79 e ^{- x} ) ^{2}} (- 79 e^{- x})) : \frac{3160 e ^{- x}}{( 1 + 79 e ^{- x} ) ^{2}}

= \frac{3160 e ^{- x}}{( 1 + 79 e ^{- x} ) ^{2}}

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What is the derivative of (40/(1+79e^{-x)}) ?
The derivative of (40/(1+79e^{-x)}) is (3160e^{-x})/((1+79e^{-x))^2}
What is the first derivative of (40/(1+79e^{-x)}) ?
The first derivative of (40/(1+79e^{-x)}) is (3160e^{-x})/((1+79e^{-x))^2}