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Fill in the Blank If 0 = log(xy) + a, then dydx= -y□ - Mathematics and Statistics

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प्रश्न

Fill in the Blank

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

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उत्तर

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"`

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The Concept of Derivative - Derivatives of Logarithmic Functions
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Differentiation - MISCELLANEOUS EXERCISE - 3 [पृष्ठ ९९]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 3 Differentiation
MISCELLANEOUS EXERCISE - 3 | Q II] 3) | पृष्ठ ९९

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