What is the derivative of (1.05/(1+100e^{-0.285x)}) ?

The derivative of (1.05/(1+100e^{-0.285x)}) is (29.925e^{-0.285x})/((1+100e^{-0.285x))^2}

What is the first derivative of (1.05/(1+100e^{-0.285x)}) ?

The first derivative of (1.05/(1+100e^{-0.285x)}) is (29.925e^{-0.285x})/((1+100e^{-0.285x))^2}

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\frac{d}{d x} (\frac{1.05}{1 + 100 e ^{- 0.285 x}})

\frac{29.925 e ^{- 0.285 x}}{( 1 + 100 e ^{- 0.285 x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1.05}{1 + 100 e ^{- 0.285 x}})

Take the constant out:

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

= 1.05 \frac{d}{d x} (\frac{1}{1 + 100 e ^{- 0.285 x}})

Apply exponent rule:

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

= 1.05 \frac{d}{d x} ((1 + 100 e^{- 0.285 x})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + 100 e ^{- 0.285 x} ) ^{2}} \frac{d}{d x} (1 + 100 e^{- 0.285 x})

= - \frac{1}{( 1 + 100 e ^{- 0.285 x} ) ^{2}} \frac{d}{d x} (1 + 100 e^{- 0.285 x})

\frac{d}{d x} (1 + 100 e^{- 0.285 x}) = - 28.5 e^{- 0.285 x}

= 1.05 (- \frac{1}{( 1 + 100 e ^{- 0.285 x} ) ^{2}} (- 28.5 e^{- 0.285 x}))

Simplify

1.05 (- \frac{1}{( 1 + 100 e ^{- 0.285 x} ) ^{2}} (- 28.5 e^{- 0.285 x})) : \frac{29.925 e ^{- 0.285 x}}{( 1 + 100 e ^{- 0.285 x} ) ^{2}}

= \frac{29.925 e ^{- 0.285 x}}{( 1 + 100 e ^{- 0.285 x} ) ^{2}}

\int_{0}^{1.2} 1 - \frac{y}{2} d y

\frac{7 s}{s ^{2} - 2 s + 10}

\int \frac{t}{t + 1} d t

\int \frac{2 x + 5}{x ^{2} - 4 x + 13} d x

y 2 y = 4 x + 8

What is the derivative of (1.05/(1+100e^{-0.285x)}) ?
The derivative of (1.05/(1+100e^{-0.285x)}) is (29.925e^{-0.285x})/((1+100e^{-0.285x))^2}
What is the first derivative of (1.05/(1+100e^{-0.285x)}) ?
The first derivative of (1.05/(1+100e^{-0.285x)}) is (29.925e^{-0.285x})/((1+100e^{-0.285x))^2}