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Manipal MET2010MathematicsDifferentiation

If x^y=e^ x-y , then d y d x is equal to

Options

  1. Ax (1+ x)^2
  2. Bx-y (1+ x)
  3. Cx-y (1+ x)^2
  4. D1 (1+ x)

Correct answer

A. x (1+ x)^2

Step-by-step solution

We have, x^y=e^ x-y y x=(x-y) e=x-y y= x 1+ x d y d x = (1+ x) 1-x 1 x (1+ x)^2 = x (1+ x)^2

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