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

The derivative of (sqrt(x)/(sqrt(x-1))) is -1/(2sqrt(x)(x-1)^{3/2)}

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

The first derivative of (sqrt(x)/(sqrt(x-1))) is -1/(2sqrt(x)(x-1)^{3/2)}

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

- \frac{1}{2 x ( x - 1 ) ^{\frac{3}{2}}}

Solution steps

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

Simplify

\frac{x}{x - 1} : \frac{x}{x - 1}

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 \frac{x}{x - 1}} (- \frac{1}{( x - 1 ) ^{2}}) : - \frac{1}{2 x ( x - 1 ) ^{\frac{3}{2}}}

= - \frac{1}{2 x ( x - 1 ) ^{\frac{3}{2}}}

x^{2} y^{^{'}} + 2 x y = 5 y^{4}

\frac{\partial}{\partial x} (x^{3} + 2^{y} + x^{y})

\frac{\partial}{\partial x} (5 x y^{5} z)

\frac{d}{d x} (x e^{6 x})

- \frac{x ^{2}}{4} + \frac{22}{4}

What is the derivative of (sqrt(x)/(sqrt(x-1))) ?
The derivative of (sqrt(x)/(sqrt(x-1))) is -1/(2sqrt(x)(x-1)^{3/2)}
What is the first derivative of (sqrt(x)/(sqrt(x-1))) ?
The first derivative of (sqrt(x)/(sqrt(x-1))) is -1/(2sqrt(x)(x-1)^{3/2)}