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MHT CET202617 April 2026Morning ShiftMathematicsDifferentiationActual

If y = x 7^x , then the value of dx dy when x = 1 is

Options

  1. A7( 7 + 1)
  2. B7 + 1
  3. C1 7( 7 + 1)
  4. D1 7 + 1

Correct answer

C. 1 7( 7 + 1)

Step-by-step solution

Given y = x 7^x Differentiating with respect to x using the product rule: dy dx = 1 7^x + x 7^x 7 dy dx = 7^x(1 + x 7) Substituting x = 1 : . dy dx |_ x=1 = 7^1(1 + 1 7) = 7(1 + 7) Since dx dy = 1 dy dx : . dx dy |_ x=1 = 1 7(1 + 7) Answer: 1 7( 7 + 1)

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