InterviewSolution
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InterviewSolution
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यदि `e^(x)+e^(y)=e^(x+y)` हो,तो सिद्ध कीजिए कि `(dy)/(dx)=-(e^(x)(e^(y)-1))/(e^(y)(e^(x)-1))` |
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Answer» `e^(x)+e^(y)=e^(x+y)` दोनों पक्षों का x के सापेक्ष अवकलन करने पर, `d/(dx)(e^(x)+e^(y))=d/(dx)(e^(x+y))` `rArrd/(dx)(e^(x))+d/(dx)(e^(y))=e^(x+y)d/(dx)(x+y)` `rArre^(x)+e^(y)(dy)/(dx)=e^(x+y)(1+(dy)/(dx))` `rArre^(x)+(e^(y)-e^(x+y))(dy)/(dx)=e^(x+y)` `rArr(e^(y)-e^(x+y))(dy)/(dx)=e^(x+y)-e^(x)` `rArre^(y)(1-e^(x))(dy)/(dx)=e^(x)(e^(y)-1)` `rArr(dy)/(dx)=(e^(x)(e^(y)-1))/(e^(y)(1-e^(x)))` `rArr(dy)/(dx)=-(e^(x)(e^(y)-1))/(e^(y)(e^(x)-1))` यही सिद्ध करना था| |
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