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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

y = e^{4} x^{2} + 18

f (x) = (\frac{8 x + 7}{9 x ^{2} + 6})

y = cos (x), y = sin (x)

7 e^{x}, 7 x e^{x^{2}}, [0, 1]

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

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