What is the derivative of (250/(1+4e^{-0.75x)}) ?

The derivative of (250/(1+4e^{-0.75x)}) is (750e^{-0.75x})/((1+4e^{-0.75x))^2}

What is the first derivative of (250/(1+4e^{-0.75x)}) ?

The first derivative of (250/(1+4e^{-0.75x)}) is (750e^{-0.75x})/((1+4e^{-0.75x))^2}

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\frac{d}{d x} (\frac{250}{1 + 4 e ^{- 0.75 x}})

\frac{750 e ^{- 0.75 x}}{( 1 + 4 e ^{- 0.75 x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{250}{1 + 4 e ^{- 0.75 x}})

Take the constant out:

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

= 250 \frac{d}{d x} (\frac{1}{1 + 4 e ^{- 0.75 x}})

Apply exponent rule:

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

= 250 \frac{d}{d x} ((1 + 4 e^{- 0.75 x})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + 4 e ^{- 0.75 x} ) ^{2}} \frac{d}{d x} (1 + 4 e^{- 0.75 x})

= - \frac{1}{( 1 + 4 e ^{- 0.75 x} ) ^{2}} \frac{d}{d x} (1 + 4 e^{- 0.75 x})

\frac{d}{d x} (1 + 4 e^{- 0.75 x}) = - 3 e^{- 0.75 x}

= 250 (- \frac{1}{( 1 + 4 e ^{- 0.75 x} ) ^{2}} (- 3 e^{- 0.75 x}))

Simplify

250 (- \frac{1}{( 1 + 4 e ^{- 0.75 x} ) ^{2}} (- 3 e^{- 0.75 x})) : \frac{750 e ^{- 0.75 x}}{( 1 + 4 e ^{- 0.75 x} ) ^{2}}

= \frac{750 e ^{- 0.75 x}}{( 1 + 4 e ^{- 0.75 x} ) ^{2}}

\int \frac{- e ^{4 x}}{4 x} d x

\int 27 x^{2} cos (3 x) d x

\int - \frac{1000}{x ^{2}} d x

\int_{0}^{3} \frac{1}{3 - x} d x

\int cos (x) e^{- 3 x} d x

What is the derivative of (250/(1+4e^{-0.75x)}) ?
The derivative of (250/(1+4e^{-0.75x)}) is (750e^{-0.75x})/((1+4e^{-0.75x))^2}
What is the first derivative of (250/(1+4e^{-0.75x)}) ?
The first derivative of (250/(1+4e^{-0.75x)}) is (750e^{-0.75x})/((1+4e^{-0.75x))^2}