What is the derivative of x/(1-e^t(1-x)) ?

The derivative of x/(1-e^t(1-x)) is (1-e^t)/((1-e^t(1-x))^2)

What is the first derivative of x/(1-e^t(1-x)) ?

The first derivative of x/(1-e^t(1-x)) is (1-e^t)/((1-e^t(1-x))^2)

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\frac{d}{d x} (\frac{x}{1 - e ^{t} ( 1 - x )})

\frac{1 - e ^{t}}{( 1 - e ^{t} ( 1 - x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{1 - e ^{t} ( 1 - x )})

Treat

t

as a constant

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

= \frac{1 \cdot ( 1 - e ^{t} ( 1 - x ) ) - e ^{t} x}{( 1 - e ^{t} ( 1 - x ) ) ^{2}}

Simplify

\frac{1 \cdot ( 1 - e ^{t} ( 1 - x ) ) - e ^{t} x}{( 1 - e ^{t} ( 1 - x ) ) ^{2}} : \frac{1 - e ^{t}}{( 1 - e ^{t} ( 1 - x ) ) ^{2}}

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

\frac{[ 100 \cdot ( s + 1 ) ]}{[ ( s ^{2} ) \cdot ( s + 10 ) ]}

(2 i, 3 j, - 4 k) (i - 3 j + k)

\frac{8 ( 8 - x )}{64 - x}

(- 10 + 11) (- 4 + 10)

\frac{( ( x + y ) ( ( x + y ) + 1 ) - ( x x + 1 ) )}{y}

What is the derivative of x/(1-e^t(1-x)) ?
The derivative of x/(1-e^t(1-x)) is (1-e^t)/((1-e^t(1-x))^2)
What is the first derivative of x/(1-e^t(1-x)) ?
The first derivative of x/(1-e^t(1-x)) is (1-e^t)/((1-e^t(1-x))^2)