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KCET2020MathematicsApplication of Derivatives

If (x e)^ y =e^ y , then d y d x is

Options

  1. Ax (1+ x)²
  2. B1 (1+ x)²
  3. Cx (1+ x)
  4. De^ x x(y-1)

Correct answer

A. x (1+ x)²

Step-by-step solution

We have, (x e)^ y =e^ x Taking log on both sides at base e , we get aligned y (x e) &=x e & y( x+ e) &=x ( _ e e=1 ) y &= x x+1 aligned On differentiating both sides w.r.t. x , we get aligned d y d x &= ( x+1)-x ( 1 x +0 ) ( x+1)² d y d x &= x ( x+1)² aligned

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