What is the derivative of (ce^t)/(1+ce^t) ?

The derivative of (ce^t)/(1+ce^t) is (ce^t)/((1+ce^t)^2)

What is the first derivative of (ce^t)/(1+ce^t) ?

The first derivative of (ce^t)/(1+ce^t) is (ce^t)/((1+ce^t)^2)

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derivative of

\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{\partial}{\partial x} ((\frac{( x + 4 )}{y + 5})^{\frac{1}{2}})

\int (x^{2} + 7 x - 5) cos (2 x) d x

f (x) = x (2 x - 1) (3 x + 2)

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

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = - 3, y^{^{'}} (0) = - 1

What is the derivative of (ce^t)/(1+ce^t) ?
The derivative of (ce^t)/(1+ce^t) is (ce^t)/((1+ce^t)^2)
What is the first derivative of (ce^t)/(1+ce^t) ?
The first derivative of (ce^t)/(1+ce^t) is (ce^t)/((1+ce^t)^2)