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AP EAMCET2001MathematicsDifferentiation

If h(x)=x^ x^x , then at x=1, h^ (x) h(x) is equal to

Options

  1. Ah(x)
  2. B1 h(x)
  3. C1+ h(x)
  4. D- h(x)

Correct answer

C. 1+ h(x)

Step-by-step solution

We have, aligned h(x) & =x^ x^ x^* h(x) & =x^x x aligned On differentiating w. r. t. x , we get as aligned h^ (x) h(x) & =x^x 1 x +x^x(1+ x) x & =x^ x-1 +(1+ x) h(x)[ from Eq. (i) ] & =1+(1+ 1) h(x) & =1+ h(x) aligned

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