InterviewSolution
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InterviewSolution
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यदि `y=sin^(-1)[xsqrt(1-x)-sqrtxsqrt(1-x^(2))]` हो,तो `(dy)/(dx)` ज्ञात कीजिए। |
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Answer» `y=sin^(-1)[xsqrt(1-x)-sqrtxsqrt(1-x^(2))]` `rArry=sin^(-1)[sqrt(1-(sqrtx)^(2))-sqrtxsqrt(1-x^(2))]` `x=sintheta` और `sqrtx=sinphi` रखने पर, ltbr gt`y=sin^(-1)[sinthetasqrt(1-sin^(2)phi)-sinphisqrt(1-sin^(2)theta)]` `rArry=sin^(-1)[sinthetacosphi-sinphicostheta]` `rArry=sin^(-1)[sin(theta-phi)]` `rArry=theta-phi` `rArry=sin^(-1)x-sin^(-1)sqrtx` दोनों पक्षों का x के सापेक्ष अवकलन करने पर, `(dy)/(dx)=d/(dx)(sin^(-1)x)-d/(dx)(sin^(-1)sqrtx)` `(du)/(dx)=1/(sqrt(1-x^(2)))-1/(1-(sqrtx)^(2)).d/(dx)(sqrtx)` `(dy)/(dx)=1/(sqrt(1-x^(2)))-1/(1-x)xx1/(2sqrtx)` `therefore(dy)/(dx)=1/(sqrt(1-x^(2)))-1/(2sqrtx(1-x))` |
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