What is the derivative of (300/(3+17e^{-0.0625x)}) ?

The derivative of (300/(3+17e^{-0.0625x)}) is (318.75e^{-0.0625x})/((3+17e^{-0.0625x))^2}

What is the first derivative of (300/(3+17e^{-0.0625x)}) ?

The first derivative of (300/(3+17e^{-0.0625x)}) is (318.75e^{-0.0625x})/((3+17e^{-0.0625x))^2}

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\frac{d}{d x} (\frac{300}{3 + 17 e ^{- 0.0625 x}})

\frac{318.75 e ^{- 0.0625 x}}{( 3 + 17 e ^{- 0.0625 x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{300}{3 + 17 e ^{- 0.0625 x}})

Take the constant out:

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

= 300 \frac{d}{d x} (\frac{1}{3 + 17 e ^{- 0.0625 x}})

Apply exponent rule:

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

= 300 \frac{d}{d x} ((3 + 17 e^{- 0.0625 x})^{- 1})

Apply the chain rule:

- \frac{1}{( 3 + 17 e ^{- 0.0625 x} ) ^{2}} \frac{d}{d x} (3 + 17 e^{- 0.0625 x})

= - \frac{1}{( 3 + 17 e ^{- 0.0625 x} ) ^{2}} \frac{d}{d x} (3 + 17 e^{- 0.0625 x})

\frac{d}{d x} (3 + 17 e^{- 0.0625 x}) = - 1.0625 e^{- 0.0625 x}

= 300 (- \frac{1}{( 3 + 17 e ^{- 0.0625 x} ) ^{2}} (- 1.0625 e^{- 0.0625 x}))

Simplify

300 (- \frac{1}{( 3 + 17 e ^{- 0.0625 x} ) ^{2}} (- 1.0625 e^{- 0.0625 x})) : \frac{318.75 e ^{- 0.0625 x}}{( 3 + 17 e ^{- 0.0625 x} ) ^{2}}

= \frac{318.75 e ^{- 0.0625 x}}{( 3 + 17 e ^{- 0.0625 x} ) ^{2}}

\frac{d}{d x} (x^{3} - 12 x^{2} + 45 x + 9)

x \to 2 lim (\frac{7}{x - 2})

\frac{4}{5} x^{\frac{5}{4}}

\frac{\partial}{\partial y} (- 2 y^{4} sin (2 x))

\int_{1}^{2} \frac{x ^{2} + 2}{3 x - x ^{2}} d x

What is the derivative of (300/(3+17e^{-0.0625x)}) ?
The derivative of (300/(3+17e^{-0.0625x)}) is (318.75e^{-0.0625x})/((3+17e^{-0.0625x))^2}
What is the first derivative of (300/(3+17e^{-0.0625x)}) ?
The first derivative of (300/(3+17e^{-0.0625x)}) is (318.75e^{-0.0625x})/((3+17e^{-0.0625x))^2}