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Manipal MET2011MathematicsDifferentiation

If f(x)=|x|^ | x| , then f^ (- 4 ) is equal to

Options

  1. A( 4 )^ 1 / 2 ( 2 2 4 - 2 2 )
  2. B( 4 )^ 1 / 2 ( 2 2 4 + 2 2 )
  3. C( 4 )^ 1 / 2 ( 2 2 4 - 2 2 )
  4. D( 2 2 4 + 2 2 )

Correct answer

A. ( 4 )^ 1 / 2 ( 2 2 4 - 2 2 )

Step-by-step solution

Since, f(x)=|x|^ x when x 0 aligned f(x) & =(-x)^ (- x) & =e^ - x (-x) f^ (x) & =e^ - x (-x) aligned (- x (-x)- x x ) f^ (x)=(-x)^ - x (- x (-x)- x x ) f^ (- 4 )= ( 4 )^ 1 / 2 (- 1 2 4 + 4 (- 1 2 ) ) aligned & & = ( 4 )^ 1 / 2 ( 2 2 4 - 2 2 ) aligned

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