InterviewSolution
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InterviewSolution
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यदि `y=log{e^(x)((x-2)/(x+2))^(3/4)}`, तब दर्शाइए की- `(dy)/(dx)=(x^(2)-1)/(x^(2)-4)` |
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Answer» दिया गया है- `y=log{e^(x)((x-2)/(x+2))^(3/4)}` `rArry=loge^(x)+log((x-2)/(x+2))^(3/4)` `rArry=loge^(x)+3/4log((x-2)/(x+2))` `rArry=x+3/4[log(x-2)-log(x+2)]` दोनों पक्षों का x के सापेक्ष अवकलन करने पर, `(dy)/(dx)=d/(dx)(x)+3/4[d/(dx)log(x-2)-d/(dx)log(x+2)]` `rArr(dy)/(dx)=1+3/4[1/(x-2)d/(dx)(x-2)-1/(x+2)d/(dx)(x+2)]` `rArr(dy)/(dx)=1+3/4[1/(x-2)xx1-1/(x+2)xx1]` `rArr(dy)/(dx)=1+3/4[1/(x-2)-1/(x+2)]` `rArr(dy)/(dx)=1+3/4[(x+2-x+2)/((x-2)(x+2))]` `rArr(dy)/(dx)=1+3/4xx4/(x^(2)-4)` `rArr(dy)/(dx)=1+3/(x^(2)-4)` `rArr(dy)/(dx)=((x^(2)-4)+3)/(x^(2)-4)` `rArr(dy)/(dx)=(x^(2)-1)/(x^(2)-4)` यही सिद्ध करना था |
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