What is the derivative of arccot(x+arccot(1/x)) ?

The derivative of arccot(x+arccot(1/x)) is 0

What is the first derivative of arccot(x+arccot(1/x)) ?

The first derivative of arccot(x+arccot(1/x)) is 0

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

0

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (arccot (x)) + \frac{d}{d x} (arccot (\frac{1}{x}))

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

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

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

Simplify

- \frac{1}{x ^{2} + 1} + \frac{1}{1 + x ^{2}} : 0

= 0

What is the derivative of arccot(x+arccot(1/x)) ?
The derivative of arccot(x+arccot(1/x)) is 0
What is the first derivative of arccot(x+arccot(1/x)) ?
The first derivative of arccot(x+arccot(1/x)) is 0