Question

If x = t.logt, y = t^t, then show that `("d"y)/("d"x)` = t^t 

Answer 1

x = t.logt    ......(i)

y = t^t     ......(ii)

Taking logarithm of both sides, we get

log y = log t^t

∴ 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)` = t^t     ......[From (ii)]