InterviewSolution
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InterviewSolution
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यदि `sin(xy)+x/y=x^(2)-y` हो,तो `(dy)/(dx)` ज्ञात कीजिए । |
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Answer» `sin(xy)+x/y=x^(2)-y` दोनों पक्षों का x के सापेक्ष अवकलन करने पर, `d/(dx)sin(xy)+d/(dx)(x/y)=d/(dx)(x^(2))-(dy)/(dx)` `rArrcos(xy)d/(dx)(xy)+(y-x(dy)/(dx))/(y^(2))=2x-(dy)/(dx)` `rArrcos(xy)(x(dy)/(dx)+y)+1/y-x/(y^(2))(dy)/(dx)=2x-(dy)/(dx)` `rArrxcos(xy)(dy)/(dx)+ycos(xy)+1/y-x/(y^(2))(dy)/(dx)=2x-(dy)/(dx)` `rArr[xcos(xy)-x/(y^(2))+1](dy)/(dx)` `=2x-1/y-ycos(xy)` `rArr[xy^(2)cos(xy)-x+y^(2)](dy)/(dx)` `=[2x-1/y-ycos(xy)]y^(2)` `rArr[xy^(2)cos(xy)-x+y^(2)](dy)/(dx)` `=[2xy^(2)-y-y^(3)cos(xy)]` ltbr gt`rArr(dy)/(dx)=(2xy^(2)-y-y^(3)cos(xy))/(xy^(2)cos(xy)-x+y^(2))` |
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