If y = xx, what is  at x = 1 equal to?

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Answer (Detailed Solution Below)

Option 2 : 1
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Detailed Solution

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Concept:

Suppose that we have two functions f(x) and g(x) and they are both differentiable.

  • Chain Rule: 
  • Product Rule: 

 

Calculation:

y = xx

Taking log both sides, we get

⇒ log y = log xx                          (∵ log mn = n log m)

⇒ log y = x log x

Differentiating with respect to x, we get

put x = 1

                (∵ log 1 = 0)

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