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KCET2016MathematicsDifferentiation

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

Options

  1. A( x (x-y) )
  2. B( e^ x x^ x-y )
  3. C( x (1+ x)² )
  4. D( 1 y - 1 x-y )

Correct answer

C. ( x (1+ x)² )

Step-by-step solution

Given that, ( x^ y =e^ x-y ) Taking log both sides, we get [ array l y x=x-y y(1+ x)=x y= x (1+ x) array ] [ array l So, d y d x = (1+ x)-x ( 1 x ) (1+ x)² = x (1+ x)² array ]

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