The root x power of Y is equal to the root y power of X

The root x power of Y is equal to the root y power of X

Y ^ (√ x) = x ^ (√ y) take the logarithm LNY * √ x = LNX √ y on both sides, that is, y ^ (- 1 / 2) LNY = x ^ (- 1 / 2) LNX, for X derivation, remember that y is the function of X (y is the intermediate variable in the derivation) y '* (- 1 / 2) y ^ (- 3 / 2) LNY + y ^ (- 1 / 2) y' / y = (- 1 / 2) x ^ (- 3 / 2) LNX + x ^ (- 1 / 2) / X  y '= [x ^ (- 3 / 2) lnx-2x ^ (- 3 / 2)]