What is the derivative of arctan^2(1/x) ?

The derivative of arctan^2(1/x) is -(2arctan(1/x))/(1+x^2)

What is the first derivative of arctan^2(1/x) ?

The first derivative of arctan^2(1/x) is -(2arctan(1/x))/(1+x^2)

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\frac{d}{d x} (arctan^{2} (\frac{1}{x}))

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

Solution steps

\frac{d}{d x} (arctan^{2} (\frac{1}{x}))

Apply the chain rule:

2 arctan (\frac{1}{x}) \frac{d}{d x} (arctan (\frac{1}{x}))

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

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

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

Simplify

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

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

\frac{d}{d x} (2 sin (x) - 3 cos (x))

\int 20 arctan (x) d x

\frac{d}{d x} (5 e^{- x} - 6 e^{x})

y = 4 + 3 x

\frac{d}{d x} ((ln (x))^{l n (x)})

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