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KCET2020MathematicsDifferentiation

If 2^ x +2^ y =2^ x+y , then d y d x is

Options

  1. A2^ y-x
  2. B-2^ y-x
  3. C2^ x-y
  4. D2^ y -1 2^ x -1

Correct answer

B. -2^ y-x

Step-by-step solution

We have, 2^ x +2^ y =2^ x+y ...(i) On differentiating Eq. (i) w.r.t. x , we get 2^ x 2+2^ y 2 d y d x =2^ x+y 2 (1+ d y d x ) 2^ x +2^ y d y d x =2^ x+y (1+ d y d x ) 2^ x -2^ x+y = d y d x (2^ x+y -2^ y ) -2^ y = d y d x (2^ x ) d y d x =-2^ y / 2^ x =-2^ y-x

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