What is the d/(dt)(1/(1+24e^{-0.28t)}) ?

The d/(dt)(1/(1+24e^{-0.28t)}) is (6.72e^{-0.28t})/((1+24e^{-0.28t))^2}

What is the first d/(dt)(1/(1+24e^{-0.28t)}) ?

The first d/(dt)(1/(1+24e^{-0.28t)}) is (6.72e^{-0.28t})/((1+24e^{-0.28t))^2}

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\frac{d}{d t} (\frac{1}{1 + 24 e ^{- 0.28 t}})

\frac{6.72 e ^{- 0.28 t}}{( 1 + 24 e ^{- 0.28 t} ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{1}{1 + 24 e ^{- 0.28 t}})

Apply exponent rule:

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

= \frac{d}{d t} ((1 + 24 e^{- 0.28 t})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + 24 e ^{- 0.28 t} ) ^{2}} \frac{d}{d t} (1 + 24 e^{- 0.28 t})

= - \frac{1}{( 1 + 24 e ^{- 0.28 t} ) ^{2}} \frac{d}{d t} (1 + 24 e^{- 0.28 t})

\frac{d}{d t} (1 + 24 e^{- 0.28 t}) = - 6.72 e^{- 0.28 t}

= - \frac{1}{( 1 + 24 e ^{- 0.28 t} ) ^{2}} (- 6.72 e^{- 0.28 t})

Simplify

- \frac{1}{( 1 + 24 e ^{- 0.28 t} ) ^{2}} (- 6.72 e^{- 0.28 t}) : \frac{6.72 e ^{- 0.28 t}}{( 1 + 24 e ^{- 0.28 t} ) ^{2}}

= \frac{6.72 e ^{- 0.28 t}}{( 1 + 24 e ^{- 0.28 t} ) ^{2}}

x y^{^{'}} + 2 y = 3 x, y (1) = 5

\int \frac{x}{( x ^{2} + 2 ) ^{\frac{4}{3}}} d x

y^{^{'}} = 3 y - y^{2}

c x

y^{^{'}} - \frac{4}{x} y = \frac{y ^{3}}{x ^{3}}, y (1) = 1

What is the d/(dt)(1/(1+24e^{-0.28t)}) ?
The d/(dt)(1/(1+24e^{-0.28t)}) is (6.72e^{-0.28t})/((1+24e^{-0.28t))^2}
What is the first d/(dt)(1/(1+24e^{-0.28t)}) ?
The first d/(dt)(1/(1+24e^{-0.28t)}) is (6.72e^{-0.28t})/((1+24e^{-0.28t))^2}