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derivative of sqrt(x/(x-1))

Solution

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

Solution

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

Solution steps

\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}}}

Graph

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Frequently Asked Questions (FAQ)

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