What is the d/(dt)((ce^t)/(1+ce^t)) ?

The d/(dt)((ce^t)/(1+ce^t)) is (ce^t)/((1+ce^t)^2)

What is the first d/(dt)((ce^t)/(1+ce^t)) ?

The first d/(dt)((ce^t)/(1+ce^t)) is (ce^t)/((1+ce^t)^2)

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Popular >

\frac{d}{d t} (\frac{c e ^{t}}{1 + c e ^{t}})

\frac{c e ^{t}}{( 1 + c e ^{t} ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{c e ^{t}}{1 + c e ^{t}})

Take the constant out:

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

= c \frac{d}{d t} (\frac{e ^{t}}{1 + c e ^{t}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d t} (e^{t}) = e^{t}

\frac{d}{d t} (1 + c e^{t}) = c e^{t}

= c \frac{e ^{t} ( 1 + c e ^{t} ) - c e ^{t} e ^{t}}{( 1 + c e ^{t} ) ^{2}}

Simplify

c \frac{e ^{t} ( 1 + c e ^{t} ) - c e ^{t} e ^{t}}{( 1 + c e ^{t} ) ^{2}} : \frac{c e ^{t}}{( 1 + c e ^{t} ) ^{2}}

= \frac{c e ^{t}}{( 1 + c e ^{t} ) ^{2}}

\frac{d y}{d t} = \frac{( y + 1 )}{( t + 1 )}

\int_{4}^{9} \frac{x - 3}{x} d x

\int sec^{4} (x t a) n^{2} x d x

\int \frac{x}{1 + x} d x

x \to 1 lim (\frac{1}{( x - 1 )})

What is the d/(dt)((ce^t)/(1+ce^t)) ?
The d/(dt)((ce^t)/(1+ce^t)) is (ce^t)/((1+ce^t)^2)
What is the first d/(dt)((ce^t)/(1+ce^t)) ?
The first d/(dt)((ce^t)/(1+ce^t)) is (ce^t)/((1+ce^t)^2)