What is the derivative of (12800)/(1+10e^{-0.5x)} ?

The derivative of (12800)/(1+10e^{-0.5x)} is (64000e^{-0.5x})/((1+10e^{-0.5x))^2}

What is the first derivative of (12800)/(1+10e^{-0.5x)} ?

The first derivative of (12800)/(1+10e^{-0.5x)} is (64000e^{-0.5x})/((1+10e^{-0.5x))^2}

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derivative of

\frac{12800}{1 + 10 e ^{- 0.5 x}}

\frac{64000 e ^{- 0.5 x}}{( 1 + 10 e ^{- 0.5 x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{12800}{1 + 10 e ^{- 0.5 x}})

Take the constant out:

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

= 12800 \frac{d}{d x} (\frac{1}{1 + 10 e ^{- 0.5 x}})

Apply exponent rule:

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

= 12800 \frac{d}{d x} ((1 + 10 e^{- 0.5 x})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + 10 e ^{- 0.5 x} ) ^{2}} \frac{d}{d x} (1 + 10 e^{- 0.5 x})

= - \frac{1}{( 1 + 10 e ^{- 0.5 x} ) ^{2}} \frac{d}{d x} (1 + 10 e^{- 0.5 x})

\frac{d}{d x} (1 + 10 e^{- 0.5 x}) = - 5 e^{- 0.5 x}

= 12800 (- \frac{1}{( 1 + 10 e ^{- 0.5 x} ) ^{2}} (- 5 e^{- 0.5 x}))

Simplify

12800 (- \frac{1}{( 1 + 10 e ^{- 0.5 x} ) ^{2}} (- 5 e^{- 0.5 x})) : \frac{64000 e ^{- 0.5 x}}{( 1 + 10 e ^{- 0.5 x} ) ^{2}}

= \frac{64000 e ^{- 0.5 x}}{( 1 + 10 e ^{- 0.5 x} ) ^{2}}

What is the derivative of (12800)/(1+10e^{-0.5x)} ?
The derivative of (12800)/(1+10e^{-0.5x)} is (64000e^{-0.5x})/((1+10e^{-0.5x))^2}
What is the first derivative of (12800)/(1+10e^{-0.5x)} ?
The first derivative of (12800)/(1+10e^{-0.5x)} is (64000e^{-0.5x})/((1+10e^{-0.5x))^2}