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

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

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

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

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

- \frac{1}{2 x x - 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{1}{2 x x - 1}

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