What is the derivative of (3x/(1-x)) ?

The derivative of (3x/(1-x)) is 3/((1-x)^2)

What is the first derivative of (3x/(1-x)) ?

The first derivative of (3x/(1-x)) is 3/((1-x)^2)

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\frac{d}{d x} (\frac{3 x}{1 - x})

\frac{3}{( 1 - x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x}{1 - x})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{x}{1 - x})

Apply the Quotient Rule:

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

= 3 \cdot \frac{\frac{d x}{d x} ( 1 - x ) - \frac{d}{d x} ( 1 - x ) x}{( 1 - x ) ^{2}}

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

\frac{d}{d x} (1 - x) = - 1

= 3 \cdot \frac{1 \cdot ( 1 - x ) - ( - 1 ) x}{( 1 - x ) ^{2}}

Simplify

3 \cdot \frac{1 \cdot ( 1 - x ) - ( - 1 ) x}{( 1 - x ) ^{2}} : \frac{3}{( 1 - x ) ^{2}}

= \frac{3}{( 1 - x ) ^{2}}

x \to 4 lim (- \frac{4}{- x + 4})

\int e^{\frac{1}{x}} d x

\int \frac{x}{4 + x ^{2}} d x

(5 + 6 x)^{2}

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

What is the derivative of (3x/(1-x)) ?
The derivative of (3x/(1-x)) is 3/((1-x)^2)
What is the first derivative of (3x/(1-x)) ?
The first derivative of (3x/(1-x)) is 3/((1-x)^2)