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COMEDK2016MathematicsDifferentiation

The derivative of a^ x w.r.t. a^ x (a>0) is

Options

  1. Aa^ x- x
  2. Bx a^ x- x
  3. Cx a^ x- x
  4. Dx a^ x- x

Correct answer

B. x a^ x- x

Step-by-step solution

Let u=a^ x v=a^ x u= x a d u d x =u a x x=a^ x a x x and aligned v &= x a d v d x &=v a ² x &=a^ x a ² x aligned aligned d u d v &= ( d u d x ) d v d x = a^ x a x x a^ x a ² x &= a^ x x a^ x = x a^ x- x aligned

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