Maharashtra State BoardHSC Commerce 12th Board Exam
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Fill in the blank. If x = t log t and y = tt, then dydx = ____ - Mathematics and Statistics

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Fill in the Blanks

Fill in the blank.

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

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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)]

Concept: The Concept of Derivative - Derivatives of Logarithmic Functions
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 3 Differentiation
Miscellaneous Exercise 3 | Q 2.04 | Page 99
Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 3 Differentiation
Miscellaneous Exercise 3 | Q 2.09 | Page 100
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