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NDA2022MathematicsDifferentiationActual

If y= (x^x )^x , then what is the value of d y d x at x=1 ?

Options

  1. A1 2
  2. B1
  3. C2
  4. D4

Correct answer

B. 1

Step-by-step solution

y= (x^x )^x=(x)^ x^2 Taking log both side y=x^2 x aligned & 1 y d y d x =2 x x+x^2 1 x & 1 y d y d x =2 x x+x aligned aligned & put x=1, y=1 & d y d x =2 (1)+1=1 aligned

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