What is the derivative of (2sqrt(x)/(1-x)) ?

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

What is the first derivative of (2sqrt(x)/(1-x)) ?

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

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\frac{d}{d x} (\frac{2 x}{1 - x})

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

Solution steps

\frac{d}{d x} (\frac{2 x}{1 - x})

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Simplify

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

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

x \to 0 lim (\frac{0}{x})

\int u^{\frac{3}{2}} d u

\frac{d}{d x} (x + 5)

x \to 0 + lim (ln (\frac{1}{8 x}))

\frac{d}{d x} (4 sin^{3} (x))

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