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Question
If x = t.logt, y = tt, then show that `("d"y)/("d"x)` = tt
Solution
x = t.logt ......(i)
y = tt ......(ii)
Taking logarithm of both sides, we get
log y = log tt
∴ log y = t.logt
∴ log y = x ......[From (i)]
Differentiating both sides w.r.t. x, we get
`1/y*("d"y)/("d"x)` = 1
∴ `("d"y)/("d"x)` = y
∴ `("d"y)/("d"x)` = tt ......[From (ii)]
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