What is the derivative of sqrt(3/(x-1)) ?

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

What is the first derivative of sqrt(3/(x-1)) ?

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

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derivative of

\frac{3}{x - 1}

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

Solution steps

\frac{d}{d x} (\frac{3}{x - 1})

Apply the chain rule:

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

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

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

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

Simplify

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

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

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