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

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Fill in the Blanks

Fill in the blank.

If y = `"e"^"ax"`, then `"x" * "dy"/"dx" =`____

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Solution

If y = `"e"^"ax"`, then `"x" * "dy"/"dx" =` axy

Explanation:

y = `"e"^"ax"`

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

`"dy"/"dx" = "e"^"ax" * "d"/"dx" ("ax")`

`= "e"^"ax" * ("a")`

`= "a" * "e"^"ax"`

∴ `"dy"/"dx"` = ay

∴ `"x" "dy"/"dx" = "axy"`

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 2.08 | Page 100
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