Question

Differentiate sin^-1x w.r.t tan^-1x​

Answer 1

 

1−y21dxdy=1+(e−x)21.dxd(e−x)

dxdy=1−y2×1+e−2x1.(−e−x)

so, dxdy=−1+e−2x1−sin2(tan−1e−x)×e−x

or, dxdy=−1+e−2xcos(tan−1e−x)