F (x-1 / x) = LNX, find the derivative of F (x)

F (x-1 / x) = LNX, find the derivative of F (x)
Let X - (1 / x) = u, then x & # 178; - 1 = UX, X & # 178; - ux-1 = 0, x = [U + √ (U & # 178; + 4)] / 2;
[because x > 0, only a positive sign is used before the root sign]
So f (U) = ln {[U + √ (U & # 178; + 4)] / 2};
Replace u with X to get f (x) = ln {[x + √ (X & # 178; + 4)] / 2} = ln [x + √ (X & # 178; + 4)] - LN2;
∴f '(x)=[1+x/√(x²+4)]/[x+√(x²+4)]=[x+√(x²+4)]/[x²+4+x√(x²+4)].

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