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Question
Fill in the blank.
If x = t log t and y = tt, then `"dy"/"dx"` = ____
Solution
If x = t log t and y = tt, then `"dy"/"dx"` = y.
Explanation:
x = t . log t ....(i)
y = tt
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)]
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