Question

Which inverse functions have denominator \[1+x^2\] in their derivatives?

Options

• \[\sin^{-1}x\] and \[\cos^{-1}x\]

• \[\cos^{-1}x\] and \[\cot^{-1}x\]

• \[\tan^{-1}x\] and \[\cot^{-1}x\]

• \[\sec^{-1}x\] and \[\operatorname{cosec}^{-1}x\]

Answer 1

The derivatives of \[\tan^{-1}x\] and \[\cot^{-1}x\] use denominator \[1+x^2\]. The derivative of \[\cot^{-1}x\] has the negative sign.