Maharashtra State BoardHSC Commerce 12th Board Exam
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Fill in the Blank If 0 = log(xy) + a, then dydx= -y□ - Mathematics and Statistics

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Fill in the Blanks

Fill in the Blank

If 0 = log(xy) + a, then `"dy"/"dx" =  (-"y")/square`

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Solution

If 0 = log(xy) + a, then `"dy"/"dx" =  (-"y")/"x"`

Explanation:

0 = log(xy) + a

∴ log(xy) = - a

∴ log x + log y = - a

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

`1/"x" + 1/"y" "dy"/"dx" = 0`

∴ `1/"y" * "dy"/"dx" = - 1/"x"`

∴ `"dy"/"dx" = (-"y")/"x"`

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 2.03 | Page 99
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