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MHT CET202617 April 2026Evening ShiftMathematicsDifferentiationActual

If y = 1 3x + 5 , then the value of d^9 y dx^9 is..

Options

  1. A9! 3^9 (3x + 5)^9
  2. B(-1)^8 9! 3^9 (3x + 5)^9
  3. C(-1)^9 9! 3^9 (3x + 5)¹⁰
  4. D(-1)^8 8! 3^9 (3x + 5)¹⁰

Correct answer

C. (-1)^9 9! 3^9 (3x + 5)¹⁰

Step-by-step solution

Given y = (3x + 5)⁻¹ Differentiating with respect to x , we get: dy dx = -1(3x + 5)⁻² 3 d^2y dx^2 = (-1)(-2)(3x + 5)⁻³ 3^2 d^3y dx^3 = (-1)(-2)(-3)(3x + 5)⁻⁴ 3^3 Generalizing for the n -th derivative: d^ny dx^n = (-1)^n n! (3x + 5)^ -(n+1) 3^n Substituting n = 9 : d^9y dx^9 = (-1)^9 9! (3x + 5)⁻¹⁰ 3^9 = (-1)^9 9! 3^9 (3x + 5)¹⁰ Answer: (-1)^9 9! 3^9 (3x + 5)¹⁰

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