Maharashtra State BoardHSC Commerce 12th Board Exam
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Choose the correct alternative. If y = 5x . x5, then dydx=? - Mathematics and Statistics

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MCQ
Sum

Choose the correct alternative.

If y = 5x . x5, then `"dy"/"dx" = ?` 

Options

  • 5x. x(5 + log 5)

  • 5x. x(5 + log 5)

  • 5x . x(5 + x log 5)

  • 5x. x(5 + x log 5)

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Solution

5x . x(5 + x log 5)

Explanation:

y = 5x . x5

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

`"dy"/"dx" = 5^"x" * "d"/"dx" ("x"^5) + "x"^5 * "d"/"dx" (5^"x")`

`= 5^"x" * (5"x"^4) + "x"^5 (5^"x" * log 5)`

`= 5^"x" * "x"^4(5 + "x" log 5)`

Concept: Derivatives of Implicit 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 1.05 | Page 99
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