Question

Fill in the blank.

If x = t log t and y = t^t, then `"dy"/"dx"` = ____

Answer 1

If x = t log t and y = t^t, then `"dy"/"dx"` = y.

Explanation:

x = t . log t        ....(i)

y = t^t 

Taking logarithm of both sides, we get

log y = t . log t

∴ log y = x         ....[From (i)]

∴ y = `"e"^"x"`        ...(ii)

Differentiating both sides w.r.t. x, we get

`"dy"/"dx" = "e"^"x"`

∴ `"dy"/"dx" = "y"`             ....[From (ii)]