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AP EAMCET2016MathematicsDifferentiation

If y= ₂ ( ₂ x ) , then d y d x is equal to

Options

  1. A_e 2 x _e x
  2. B1 _e(2 x)^x
  3. C1 (x _e x ) _e 2
  4. D1 x ( ₂ x )^2

Correct answer

C. 1 (x _e x ) _e 2

Step-by-step solution

We have, y= ₂ ( ₂ x ) Since, _a^b= b a aligned & y= ₂ ( x 2 ) & y= x 2 2 & y= ( x)- ( 2) 2 aligned On differentiating w.r.f x , we get aligned & d y d x = 1 2 [ 1 _e x 1 x -0 ]= 1 2 _e x x & d y d x = 1 (x _e x ) _e 2 aligned

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