What is the derivative of ((x+1/(x-1))^{1/2}) ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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