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Problem 5 - Entrance Test

Find the derivative of y = x^(x^2) at x = 1.

Correct: B

Take ln: ln y = x^2 ln x. Differentiate implicitly: y'/y = 2x ln x + x^2·1/x = 2x ln x + x. At x = 1, y = 1 and ln x = 0, so y' = 1·(0 + 1) = 1.