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

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

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

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

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derivative of

\frac{x}{1 - x}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

Simplify

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

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

(y + x + 2) d x + d y = 0

\int_{0}^{π} 3 sin^{2} (2 x) d x

x \frac{d y}{d x} - y = 2 x^{2} y

\int_{0}^{1} x^{4} e^{7 x} d x

x \to - 5 - lim (\frac{- 3}{x ^{2} - 25})

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