Saved Bookmarks
| 1. |
Differentiate `tan^(-1)((sqrt(1+x^2)-1)/x) wrt sin ^(-1)((2x)/(1+x^2))dotofx (-1,1)` |
|
Answer» `u=tan^(-1)((sqrt(1+x^2)-1)/x)` `x=tantheta` `u=tan^(-1)[(sqrt(1+tan^2theta)-1)/tantheta]` `=tan^(-1)[(sectheta-1)/tantheta]` `=tan^(-1)[(1-costheta)/sintheta]` `u=tan^(-1)[tantheta2]=theta/2` `u=1/2tan^(-1)x` `du/dx=d/dx[1/2tan^(-1)x]` `v=sin^(-1)((2x)/(1+x^2))` Let `x=tantheta` `v=sin^(-1)[(2tantheta)/(1+tan^2theta)]` `(dv)/dx=2/(1+x^2)` `(du)/dv=(du)/dx*dx/(dv)` `(du)/(dv)=1/4`. |
|