What is the derivative of (200/(1+e^{5-x)}) ?

The derivative of (200/(1+e^{5-x)}) is (200e^{-x+5})/((1+e^{5-x))^2}

What is the first derivative of (200/(1+e^{5-x)}) ?

The first derivative of (200/(1+e^{5-x)}) is (200e^{-x+5})/((1+e^{5-x))^2}

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\frac{d}{d x} (\frac{200}{1 + e ^{5 - x}})

\frac{200 e ^{- x + 5}}{( 1 + e ^{5 - x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{200}{1 + e ^{5 - x}})

Take the constant out:

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

= 200 \frac{d}{d x} (\frac{1}{1 + e ^{5 - x}})

Apply exponent rule:

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

= 200 \frac{d}{d x} ((1 + e^{5 - x})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + e ^{5 - x} ) ^{2}} \frac{d}{d x} (1 + e^{5 - x})

= - \frac{1}{( 1 + e ^{5 - x} ) ^{2}} \frac{d}{d x} (1 + e^{5 - x})

\frac{d}{d x} (1 + e^{5 - x}) = - e^{- x + 5}

= 200 (- \frac{1}{( 1 + e ^{5 - x} ) ^{2}} (- e^{- x + 5}))

Simplify

200 (- \frac{1}{( 1 + e ^{5 - x} ) ^{2}} (- e^{- x + 5})) : \frac{200 e ^{- x + 5}}{( 1 + e ^{5 - x} ) ^{2}}

= \frac{200 e ^{- x + 5}}{( 1 + e ^{5 - x} ) ^{2}}

\int \frac{12 x}{( x - 1 ) ( x ^{2} + 2 x + 3 )} d x

(1.2) (3.3)

\frac{d P}{d t} = 4 Pt

\frac{d}{d x} (e^{s i n (x)} \cdot cos (x))

What is the derivative of (200/(1+e^{5-x)}) ?
The derivative of (200/(1+e^{5-x)}) is (200e^{-x+5})/((1+e^{5-x))^2}
What is the first derivative of (200/(1+e^{5-x)}) ?
The first derivative of (200/(1+e^{5-x)}) is (200e^{-x+5})/((1+e^{5-x))^2}