An advanced number problem. Derivation Y = x power + arctanx for dy / DX

An advanced number problem. Derivation Y = x power + arctanx for dy / DX

As shown in the picture

A problem of derivation of high numbers
lim(x-arc sin x)/(x sinx arc tanx) (x->0)

Lim [x → 0] (x-arcsinx) / (xsinx arctanx) = Lim [x → 0] (x-arcsinx) / (X & # 179;) [Equivalent Infinitesimal Substitution] = Lim [x → 0] [1-1 / √ (1-x & # 178;)] / (3x & # 178;) [lobita's Law] = Lim [x → 0] [- # 189; · (- 2x) · (1-x & # 178;) ^ (- 3 / 2)] / (6x)

Help me solve a derivation problem in advanced mathematics,
Let y = y (x) be determined by the equation x ^ y = y ^ x, then dy / DX =?

Ln（X^Y)=Ln(Y^X)
Ylnx = xlny / / Y represents the derivative of Y
yLnX+Y/X=LnY+X/Y*y
y(LnX-X/Y)=LnY-Y/X
Simplify the rest of yourself