What is the derivative of 20(1+e^{10-x}^{-1}) ?

The derivative of 20(1+e^{10-x}^{-1}) is (20e^{-x+10})/((1+e^{10-x))^2}

What is the first derivative of 20(1+e^{10-x}^{-1}) ?

The first derivative of 20(1+e^{10-x}^{-1}) is (20e^{-x+10})/((1+e^{10-x))^2}

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\frac{d}{d x} (20 (1 + e^{10 - x})^{- 1})

\frac{20 e ^{- x + 10}}{( 1 + e ^{10 - x} ) ^{2}}

Solution steps

\frac{d}{d x} (20 (1 + e^{10 - x})^{- 1})

Take the constant out:

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

= 20 \frac{d}{d x} ((1 + e^{10 - x})^{- 1})

Apply the chain rule:

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

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

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

= 20 (- \frac{1}{( 1 + e ^{10 - x} ) ^{2}} (- e^{- x + 10}))

Simplify

20 (- \frac{1}{( 1 + e ^{10 - x} ) ^{2}} (- e^{- x + 10})) : \frac{20 e ^{- x + 10}}{( 1 + e ^{10 - x} ) ^{2}}

= \frac{20 e ^{- x + 10}}{( 1 + e ^{10 - x} ) ^{2}}

\frac{3}{x}

\frac{d N}{d t} + N = Nt e^{t + 6}

\frac{d}{d x} (\frac{x - 6}{x + 6})

\int \frac{x ^{3}}{a} - \frac{a}{x ^{2}} d x

y = e^{x}, y = e^{2 x}, x = 0, x = ln (4)

What is the derivative of 20(1+e^{10-x}^{-1}) ?
The derivative of 20(1+e^{10-x}^{-1}) is (20e^{-x+10})/((1+e^{10-x))^2}
What is the first derivative of 20(1+e^{10-x}^{-1}) ?
The first derivative of 20(1+e^{10-x}^{-1}) is (20e^{-x+10})/((1+e^{10-x))^2}