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COMEDK202510 May 2025Evening ShiftMathematicsDifferentiationActual

Differentiate _a x with respect to a^x

Options

  1. Aa^x x
  2. B1 x a^x
  3. Ca^x x( a)^2
  4. D1 x a^x( a)^2

Correct answer

D. 1 x a^x( a)^2

Step-by-step solution

Let u = _ a x and v = a^ x . We need to find du dv = du/dx dv/dx . Using the change of base formula, u = _ a x = x a . Differentiating u with respect to x : du dx = 1 a 1 x = 1 x a . Differentiating v = a^ x with respect to x : dv dx = a^ x a . Therefore, du dv = 1/(x a) a^ x a = 1 x a^ x ( a)² . Since ( a)² = ( _ e a)² , this is equivalent to 1 x a^ x ( a)² . Answer: 1 x a^x( a)^2

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