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

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

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

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

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derivative of

arctan (x) + arctan (\frac{1}{x})

0

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (arctan (\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

\frac{d}{d x} (\frac{2 x}{5 x - 1})

\frac{d}{d x} (\frac{375}{x ^{4}})

\int \frac{tan ^{3} ( x )}{cos ^{2} ( x )} d x

\int - 3 e^{- x} d x

\int (x^{2} - 4)^{4} (2 x) d x

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