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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to - 1 lim (2 x^{2} + 6 x - 1)

x \to 2 lim (\frac{5}{∣ 2 - x ∣})

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

f (x) = e^{x} arctan (x)

2 sin (x) + sin^{2} (x)

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