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

1 Answer

Jun 4, 2018

#f'(x) = -1/(1+x^2)#

Explanation:

#f(x) = arctan(1/x)#

Apply standard derivative and chain rule.

#f'(x) = 1/((1/x)^2+1) * d/dx (1/x)#

#= 1/(1/x^2+1) * (-1/x^2)#

#= x^2/(1+x^2) * (-1/x^2)#

# = -1/(1+x^2)#

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