Differentiate with respect to x :

If y = sin^-1 ( 2x / 1 + x² ) + sec^-1 ( 1 + x² / 1 - x² ) , show that dy/dx = 4 / ( 1 + x² )

Question

Differentiate with respect to x :

If y = sin-1 ( 2x / 1 + x2 ) +
sec-1 ( 1 + x2 / 1 - x2 ) , show
that dy/dx = 4 / ( 1 + x2 )

Anuradha Sharma · Accepted Answer

Let y =sin-12x1+x2+sec-11+x21-x2=sin-12x1+x2+cos-11-x21+x2Let x = tanθ=sin-12 tanθ1+ tan2θ+cos-11- tan2θ1+ tan2θ=sin-1sin2θ+cos-1cos2θ=2θ+2θ=4θ=4tan-1xNow differentiating wrt x we get, dydx=41+x2=41+x2

Differentiate with respect to x : If y = sin-1 ( 2x / 1 + x2 ) + sec-1 ( 1 + x2 / 1 - x2 ) , show that dy/dx = 4 / ( 1 + x2 )

Differentiate with respect to x :

If y = sin^-1 ( 2x / 1 + x² ) + sec^-1 ( 1 + x² / 1 - x² ) , show that dy/dx = 4 / ( 1 + x² )