What is the derivative of (4083)/(1+6.22e^{-0.32x)} ?

The derivative of (4083)/(1+6.22e^{-0.32x)} is (8126.8032e^{-0.32x})/((1+6.22e^{-0.32x))^2}

What is the first derivative of (4083)/(1+6.22e^{-0.32x)} ?

The first derivative of (4083)/(1+6.22e^{-0.32x)} is (8126.8032e^{-0.32x})/((1+6.22e^{-0.32x))^2}

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derivative of

\frac{4083}{1 + 6.22 e ^{- 0.32 x}}

\frac{8126.8032 e ^{- 0.32 x}}{( 1 + 6.22 e ^{- 0.32 x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4083}{1 + 6.22 e ^{- 0.32 x}})

Take the constant out:

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

= 4083 \frac{d}{d x} (\frac{1}{1 + 6.22 e ^{- 0.32 x}})

Apply exponent rule:

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

= 4083 \frac{d}{d x} ((1 + 6.22 e^{- 0.32 x})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + 6.22 e ^{- 0.32 x} ) ^{2}} \frac{d}{d x} (1 + 6.22 e^{- 0.32 x})

= - \frac{1}{( 1 + 6.22 e ^{- 0.32 x} ) ^{2}} \frac{d}{d x} (1 + 6.22 e^{- 0.32 x})

\frac{d}{d x} (1 + 6.22 e^{- 0.32 x}) = - 1.9904 e^{- 0.32 x}

= 4083 (- \frac{1}{( 1 + 6.22 e ^{- 0.32 x} ) ^{2}} (- 1.9904 e^{- 0.32 x}))

Simplify

4083 (- \frac{1}{( 1 + 6.22 e ^{- 0.32 x} ) ^{2}} (- 1.9904 e^{- 0.32 x})) : \frac{8126.8032 e ^{- 0.32 x}}{( 1 + 6.22 e ^{- 0.32 x} ) ^{2}}

= \frac{8126.8032 e ^{- 0.32 x}}{( 1 + 6.22 e ^{- 0.32 x} ) ^{2}}

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What is the derivative of (4083)/(1+6.22e^{-0.32x)} ?
The derivative of (4083)/(1+6.22e^{-0.32x)} is (8126.8032e^{-0.32x})/((1+6.22e^{-0.32x))^2}
What is the first derivative of (4083)/(1+6.22e^{-0.32x)} ?
The first derivative of (4083)/(1+6.22e^{-0.32x)} is (8126.8032e^{-0.32x})/((1+6.22e^{-0.32x))^2}