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

The derivative of x/(2-sqrt(x)) is (4-sqrt(x))/(2(2-sqrt(x))^2)

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

The first derivative of x/(2-sqrt(x)) is (4-sqrt(x))/(2(2-sqrt(x))^2)

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

\frac{4 - x}{2 ( 2 - x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( 2 - x ) - ( - \frac{1}{2 x} ) x}{( 2 - x ) ^{2}} : \frac{4 - x}{2 ( 2 - x ) ^{2}}

= \frac{4 - x}{2 ( 2 - x ) ^{2}}

x^{2} + y^{2} = 25

\int \frac{8}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

x^{2} \frac{d y}{d x} + 2 x y = 5 y^{4}

\int \frac{x}{4} d x

\frac{\partial}{\partial y} (\frac{x}{y})

What is the derivative of x/(2-sqrt(x)) ?
The derivative of x/(2-sqrt(x)) is (4-sqrt(x))/(2(2-sqrt(x))^2)
What is the first derivative of x/(2-sqrt(x)) ?
The first derivative of x/(2-sqrt(x)) is (4-sqrt(x))/(2(2-sqrt(x))^2)