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Find dydx if, y = log(10x4 + 5x3 - 3x2 + 2) - Mathematics and Statistics

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प्रश्न

Find `"dy"/"dx"` if, y = log(10x4 + 5x3 - 3x2 + 2)

बेरीज
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उत्तर

y = log(10x4 + 5x3 - 3x2 + 2)

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

`"dy"/"dx" = "d"/"dx"[log (10"x"^4 + 5"x"^3 - 3"x"^2 + 2)]`

`= 1/(10"x"^4 + 5"x"^3 - 3"x"^2 + 2) * "d"/"dx" (10"x"^4 + 5"x"^3 - 3"x"^2 + 2)`

`= 1/(10"x"^4 + 5"x"^3 - 3"x"^2 + 2) * [10(4"x"^3) + 5(3"x"^2) - 3(2"x") + 0]`

∴ `"dy"/"dx" = (40"x"^3 + 15"x"^2 - 6"x")/(10"x"^4 + 5"x"^3 - 3"x"^2 + 2)`

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पाठ 3: Differentiation - EXERCISE 3.1 [पृष्ठ ९१]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 3 Differentiation
EXERCISE 3.1 | Q 2. 2) | पृष्ठ ९१

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