What is the derivative of (332/(1+8.61e^{-0.863x)}) ?

The derivative of (332/(1+8.61e^{-0.863x)}) is (2466.90276e^{-0.863x})/((1+8.61e^{-0.863x))^2}

What is the first derivative of (332/(1+8.61e^{-0.863x)}) ?

The first derivative of (332/(1+8.61e^{-0.863x)}) is (2466.90276e^{-0.863x})/((1+8.61e^{-0.863x))^2}

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\frac{d}{d x} (\frac{332}{1 + 8.61 e ^{- 0.863 x}})

\frac{2466.90276 e ^{- 0.863 x}}{( 1 + 8.61 e ^{- 0.863 x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{332}{1 + 8.61 e ^{- 0.863 x}})

Take the constant out:

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

= 332 \frac{d}{d x} (\frac{1}{1 + 8.61 e ^{- 0.863 x}})

Apply exponent rule:

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

= 332 \frac{d}{d x} ((1 + 8.61 e^{- 0.863 x})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + 8.61 e ^{- 0.863 x} ) ^{2}} \frac{d}{d x} (1 + 8.61 e^{- 0.863 x})

= - \frac{1}{( 1 + 8.61 e ^{- 0.863 x} ) ^{2}} \frac{d}{d x} (1 + 8.61 e^{- 0.863 x})

\frac{d}{d x} (1 + 8.61 e^{- 0.863 x}) = - 7.43043 e^{- 0.863 x}

= 332 (- \frac{1}{( 1 + 8.61 e ^{- 0.863 x} ) ^{2}} (- 7.43043 e^{- 0.863 x}))

Simplify

332 (- \frac{1}{( 1 + 8.61 e ^{- 0.863 x} ) ^{2}} (- 7.43043 e^{- 0.863 x})) : \frac{2466.90276 e ^{- 0.863 x}}{( 1 + 8.61 e ^{- 0.863 x} ) ^{2}}

= \frac{2466.90276 e ^{- 0.863 x}}{( 1 + 8.61 e ^{- 0.863 x} ) ^{2}}

\int 21 x^{2} d x

\int_{- 2}^{2} 3 x^{2} d x

\frac{d}{d x} (\frac{cos ( 2 x )}{1 - sin ( 2 x )})

x \to 0 lim (\frac{x ^{5} + 7 x}{x})

What is the derivative of (332/(1+8.61e^{-0.863x)}) ?
The derivative of (332/(1+8.61e^{-0.863x)}) is (2466.90276e^{-0.863x})/((1+8.61e^{-0.863x))^2}
What is the first derivative of (332/(1+8.61e^{-0.863x)}) ?
The first derivative of (332/(1+8.61e^{-0.863x)}) is (2466.90276e^{-0.863x})/((1+8.61e^{-0.863x))^2}