What is the derivative of f(x)=(20000)/(2+123e^{-0.1(x))} ?

The derivative of f(x)=(20000)/(2+123e^{-0.1(x))} is (246000e^{-0.1x})/((2+123e^{-0.1x))^2}

What is the first derivative of f(x)=(20000)/(2+123e^{-0.1(x))} ?

The first derivative of f(x)=(20000)/(2+123e^{-0.1(x))} is (246000e^{-0.1x})/((2+123e^{-0.1x))^2}

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derivative of

f (x) = \frac{20000}{2 + 123 e ^{- 0.1 (x)}}

\frac{246000 e ^{- 0.1 x}}{( 2 + 123 e ^{- 0.1 x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{20000}{2 + 123 e ^{- 0.1 x}})

Take the constant out:

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

= 20000 \frac{d}{d x} (\frac{1}{2 + 123 e ^{- 0.1 x}})

Apply exponent rule:

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

= 20000 \frac{d}{d x} ((2 + 123 e^{- 0.1 x})^{- 1})

Apply the chain rule:

- \frac{1}{( 2 + 123 e ^{- 0.1 x} ) ^{2}} \frac{d}{d x} (2 + 123 e^{- 0.1 x})

= - \frac{1}{( 2 + 123 e ^{- 0.1 x} ) ^{2}} \frac{d}{d x} (2 + 123 e^{- 0.1 x})

\frac{d}{d x} (2 + 123 e^{- 0.1 x}) = - 12.3 e^{- 0.1 x}

= 20000 (- \frac{1}{( 2 + 123 e ^{- 0.1 x} ) ^{2}} (- 12.3 e^{- 0.1 x}))

Simplify

20000 (- \frac{1}{( 2 + 123 e ^{- 0.1 x} ) ^{2}} (- 12.3 e^{- 0.1 x})) : \frac{246000 e ^{- 0.1 x}}{( 2 + 123 e ^{- 0.1 x} ) ^{2}}

= \frac{246000 e ^{- 0.1 x}}{( 2 + 123 e ^{- 0.1 x} ) ^{2}}

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What is the derivative of f(x)=(20000)/(2+123e^{-0.1(x))} ?
The derivative of f(x)=(20000)/(2+123e^{-0.1(x))} is (246000e^{-0.1x})/((2+123e^{-0.1x))^2}
What is the first derivative of f(x)=(20000)/(2+123e^{-0.1(x))} ?
The first derivative of f(x)=(20000)/(2+123e^{-0.1(x))} is (246000e^{-0.1x})/((2+123e^{-0.1x))^2}