What is the derivative of (37500)/(1+19e^{-0.6x)} ?

The derivative of (37500)/(1+19e^{-0.6x)} is (427500e^{-0.6x})/((1+19e^{-0.6x))^2}

What is the first derivative of (37500)/(1+19e^{-0.6x)} ?

The first derivative of (37500)/(1+19e^{-0.6x)} is (427500e^{-0.6x})/((1+19e^{-0.6x))^2}

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derivative of

\frac{37500}{1 + 19 e ^{- 0.6 x}}

\frac{427500 e ^{- 0.6 x}}{( 1 + 19 e ^{- 0.6 x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{37500}{1 + 19 e ^{- 0.6 x}})

Take the constant out:

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

= 37500 \frac{d}{d x} (\frac{1}{1 + 19 e ^{- 0.6 x}})

Apply exponent rule:

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

= 37500 \frac{d}{d x} ((1 + 19 e^{- 0.6 x})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + 19 e ^{- 0.6 x} ) ^{2}} \frac{d}{d x} (1 + 19 e^{- 0.6 x})

= - \frac{1}{( 1 + 19 e ^{- 0.6 x} ) ^{2}} \frac{d}{d x} (1 + 19 e^{- 0.6 x})

\frac{d}{d x} (1 + 19 e^{- 0.6 x}) = - 11.4 e^{- 0.6 x}

= 37500 (- \frac{1}{( 1 + 19 e ^{- 0.6 x} ) ^{2}} (- 11.4 e^{- 0.6 x}))

Simplify

37500 (- \frac{1}{( 1 + 19 e ^{- 0.6 x} ) ^{2}} (- 11.4 e^{- 0.6 x})) : \frac{427500 e ^{- 0.6 x}}{( 1 + 19 e ^{- 0.6 x} ) ^{2}}

= \frac{427500 e ^{- 0.6 x}}{( 1 + 19 e ^{- 0.6 x} ) ^{2}}

x \to 0 + lim (e^{x l n (x)})

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

- 384 e^{- 4 x}

\int \frac{3 x ^{2} - 10 x - 8}{x - 3} d x

\frac{d y}{d x} = - \frac{x}{y}

What is the derivative of (37500)/(1+19e^{-0.6x)} ?
The derivative of (37500)/(1+19e^{-0.6x)} is (427500e^{-0.6x})/((1+19e^{-0.6x))^2}
What is the first derivative of (37500)/(1+19e^{-0.6x)} ?
The first derivative of (37500)/(1+19e^{-0.6x)} is (427500e^{-0.6x})/((1+19e^{-0.6x))^2}