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Manipal MET2014MathematicsDifferentiation

If y=| x|^ |x| , then the value of d y d x at x= - 6 is

Options

  1. A2^ - 6 [6 2- 3 ]
  2. B2^ 6 [6 2+ 3 ]
  3. C2^ - 6 6 [6 2+ 3 ]
  4. DNone of the above

Correct answer

A. 2^ - 6 [6 2- 3 ]

Step-by-step solution

Given y=| x|^ |x| In the neighbourhood of - 6 ,|x| and | x| both are negative i.e., y=(- x)^ -x Taking log on both sides, we get y=-x (- x) aligned & aligned 1 y d y d x = & (-x) 1 - x (- x)+ (- x)(-1) & =-x x- (- x) & =-[x x+ (- x)] aligned & aligned d y d x & =-y[x x+ (- x)] aligned & aligned ( d y d x )_ x=- 6 = 2^ - 6 [6 2- 3 ] aligned aligned

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