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AP EAMCET201824 Apr 2018Morning ShiftMathematicsDifferentiationActual

d d x [x^ x +( x)^x ]=

Options

  1. Ax^ x [ x x + x x ]+( x)^xx^ x [ x x + x x ]+( x)^x[ x+x x]
  2. Bx^ x [x x+ x x]+( x)^x [ x x + ( x) ]
  3. Cx^ x [ x x + x x ]+( x)^x [x x+ ( x)]
  4. Dx^ x [ x x + x x ]+( x)^x [ x x+ ( x)]

Correct answer

A. x^ x [ x x + x x ]+( x)^xx^ x [ x x + x x ]+( x)^x[ x+x x]

Step-by-step solution

Given, d d x [x^ x +( x)^x ] Let U=x^ x , V=( x)^x aligned U & = x x 1 U d U d x & = x x + x x d U d x & =x^ x [ x x + x x ] aligned and V=( x)^x aligned & V=x x & 1 V d V d x = x+x 1 x x & d V d x =( x)^x[ x+x x] & d d x [x^ x +( x)^x ]= d U d x + d V d x &=x^ x [ x x + x x ] &+( x)^x[ x+x x] . aligned

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