What is the derivative of (500)/(12+5e^{-0.5t)} ?

The derivative of (500)/(12+5e^{-0.5t)} is (1250e^{-0.5t})/((12+5e^{-0.5t))^2}

What is the first derivative of (500)/(12+5e^{-0.5t)} ?

The first derivative of (500)/(12+5e^{-0.5t)} is (1250e^{-0.5t})/((12+5e^{-0.5t))^2}

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derivative of

\frac{500}{12 + 5 e ^{- 0.5 t}}

\frac{1250 e ^{- 0.5 t}}{( 12 + 5 e ^{- 0.5 t} ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{500}{12 + 5 e ^{- 0.5 t}})

Take the constant out:

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

= 500 \frac{d}{d t} (\frac{1}{12 + 5 e ^{- 0.5 t}})

Apply exponent rule:

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

= 500 \frac{d}{d t} ((12 + 5 e^{- 0.5 t})^{- 1})

Apply the chain rule:

- \frac{1}{( 12 + 5 e ^{- 0.5 t} ) ^{2}} \frac{d}{d t} (12 + 5 e^{- 0.5 t})

= - \frac{1}{( 12 + 5 e ^{- 0.5 t} ) ^{2}} \frac{d}{d t} (12 + 5 e^{- 0.5 t})

\frac{d}{d t} (12 + 5 e^{- 0.5 t}) = - 2.5 e^{- 0.5 t}

= 500 (- \frac{1}{( 12 + 5 e ^{- 0.5 t} ) ^{2}} (- 2.5 e^{- 0.5 t}))

Simplify

500 (- \frac{1}{( 12 + 5 e ^{- 0.5 t} ) ^{2}} (- 2.5 e^{- 0.5 t})) : \frac{1250 e ^{- 0.5 t}}{( 12 + 5 e ^{- 0.5 t} ) ^{2}}

= \frac{1250 e ^{- 0.5 t}}{( 12 + 5 e ^{- 0.5 t} ) ^{2}}

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\frac{1}{s ^{2} - 2 s - 3}

x \to 0 + lim (\frac{x - [ x ]}{[ x ] - 2 x})

\frac{d}{d x} (x^{2} lo g_{2} (7 - 6 x))

\int 6 sin^{2} (3 x) cos (3 x) ln (sin (3 x)) d x

What is the derivative of (500)/(12+5e^{-0.5t)} ?
The derivative of (500)/(12+5e^{-0.5t)} is (1250e^{-0.5t})/((12+5e^{-0.5t))^2}
What is the first derivative of (500)/(12+5e^{-0.5t)} ?
The first derivative of (500)/(12+5e^{-0.5t)} is (1250e^{-0.5t})/((12+5e^{-0.5t))^2}