InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
`tan^(-1)((sqrt(1-x^(2)))/x)` का अवकलन `cos^(-1)(2xsqrt(1-x^(2))),xne0` के सापेक्ष कीजिए |
|
Answer» माना `u=tan^(-1)((sqrt(1-x^(2)))/x)` `x=costhetarArrtheta=cos^(-1)x` रखने पर, `u=tan^(-1)((sqrt(1-cos^(2)theta))/(costheta))` `rArru=tan^(-1)((sqrt(sin^(2)theta))/(costheta))` `rArru=tan^(-1)((sintheta)/(costheta))` `rArru=tan^(-1)(tantheta)=theta` `rArru=cos^(-1)x` `therefore(du)/(dx)=(-1)/(sqrt(1-x^(2)))` और `v=cos^(-1)(2xsqrt(1-x^(2)))` `x=costhetarArrtheta=cos^(-1)x` रखने पर, `v=cos^(-1)(2costhetasqrt(1-cos^(2)theta))` `rArrv=cos^(-1)(2costhetasintheta)` `rArrv=cos^(-1)(sin2theta)` `rArrv=cos^(-1)(cos(pi/2-2theta))` `rArrv=pi/2-2theta` `rArrv=pi/2-2cos^(-1)x` `therefore(dv)/(dx)=0-2xx(-1)/(sqrt(1-x^(2)))` `=2/(sqrt(1-x^(2)))` अब, `(du)/(dx)=(du//dx)/(dv//dx)` `=-1/(sqrt(1-x^(2)))xx(sqrt(1-x^(2)))/2` `rArr(du)/(dv)=-1/2` |
|