Question

If \[t=\tan^{-1}x\], what is \[dt\]?

Options

• \[dt=\frac{1}{1+x^2}\,dx\]

• \[dt=\frac{1}{\tan^{-1}x}\,dx\]

• \[dt=(1+x^2)\,dx\]

• \[dt=\tan x\,dx\]

Answer 1

The derivative of \[\tan^{-1}x\] is \[\frac{1}{1+x^2}\]. Hence the differential is \[dt=\frac{1}{1+x^2}\,dx\].