InterviewSolution
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InterviewSolution
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`(dy)/(dx)` ज्ञात कीजिए, यदि- `y=a^(t+1/t),x=(t+1/t)^(a)` |
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Answer» यहाँ `y=a^(t+1/t)` `therefore(dy)/(dt)=d/(dt)(a^(t+1/t))` `=a^(t+1/t)d/(dt)(t+1/t).loga` `=a^(t+1/t)(1-1/(t^(2))).loga` और `x=(t+1/t)^(a)` `therefore(dx)/(dt)=a(t+1/t)^(a-1).d/(dt)(t+1/t)` `=a(t+1/t)^(a-1).(1-1/(t^(2)))` `(dx)/(dt)ne0` केवल यदि `tnepm1` अतः `tnepm1` `(dy)/(dx)=((dy)/(dt))/((dx)/(dt))=(a^(t+1/t)(1-1/(t^(2)))loga)/(a(1+1/t)^(a-1)(1-1/(t^(2))))` `rArr(dy)/(dx)=(a^(t+1/t)loga)/(a(t+1/t)^(a-1))` |
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