What is the derivative of 1/(1+24e^{-0.28x}) ?

The derivative of 1/(1+24e^{-0.28x}) is (6.72e^{-0.28x})/((1+24e^{-0.28x))^2}

What is the first derivative of 1/(1+24e^{-0.28x}) ?

The first derivative of 1/(1+24e^{-0.28x}) is (6.72e^{-0.28x})/((1+24e^{-0.28x))^2}

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\frac{d}{d x} (\frac{1}{1 + 24 e ^{- 0.28 x}})

\frac{6.72 e ^{- 0.28 x}}{( 1 + 24 e ^{- 0.28 x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{1 + 24 e ^{- 0.28 x}})

Apply exponent rule:

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

= \frac{d}{d x} ((1 + 24 e^{- 0.28 x})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + 24 e ^{- 0.28 x} ) ^{2}} \frac{d}{d x} (1 + 24 e^{- 0.28 x})

= - \frac{1}{( 1 + 24 e ^{- 0.28 x} ) ^{2}} \frac{d}{d x} (1 + 24 e^{- 0.28 x})

\frac{d}{d x} (1 + 24 e^{- 0.28 x}) = - 6.72 e^{- 0.28 x}

= - \frac{1}{( 1 + 24 e ^{- 0.28 x} ) ^{2}} (- 6.72 e^{- 0.28 x})

Simplify

- \frac{1}{( 1 + 24 e ^{- 0.28 x} ) ^{2}} (- 6.72 e^{- 0.28 x}) : \frac{6.72 e ^{- 0.28 x}}{( 1 + 24 e ^{- 0.28 x} ) ^{2}}

= \frac{6.72 e ^{- 0.28 x}}{( 1 + 24 e ^{- 0.28 x} ) ^{2}}

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\frac{d}{d x} (\frac{3}{8 x ^{\frac{5}{2}}})

y^{^{''}} + 25 y = 3 sec (5 t)

\frac{\partial}{\partial y} (ln (1 + x y) - z)

What is the derivative of 1/(1+24e^{-0.28x}) ?
The derivative of 1/(1+24e^{-0.28x}) is (6.72e^{-0.28x})/((1+24e^{-0.28x))^2}
What is the first derivative of 1/(1+24e^{-0.28x}) ?
The first derivative of 1/(1+24e^{-0.28x}) is (6.72e^{-0.28x})/((1+24e^{-0.28x))^2}