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Manipal MET2015MathematicsDifferentiation

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

Options

  1. A2^x+2^y 2^x-2^y
  2. B2^x+2^y 1+2^ x+y
  3. C2^ x-y ( 2^y-1 1-2^x )
  4. D2^ x+y -2^x 2^y

Correct answer

C. 2^ x-y ( 2^y-1 1-2^x )

Step-by-step solution

We have, 2^x+2^y=2^ x+y On differentiating both sides 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 ) aligned & (2^y-2^ x+y ) d y d x =2^ x+y -2^x & d y d x = 2^x (2^y-1 ) 2^y (1-2^x ) =2^ x-y ( 2^y-1 1-2^x ) aligned

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