Maths Question

Use y' to represent dy/dx
a) y= (lnx)^x
lny = xln(ln x)
y'/y = ln(ln x) + (x)(1/ln x)(1/x)
y'/y = ln(ln x) + 1/ln x
y' = (ln x)^x[ln(ln x) + 1/ln x]
y' = [(ln x)^x][ln(ln x)] + (ln x)^(x-1)
b) y= (x+1/x)^x
ln y = xln(x + 1/x)
y'/y = ln(x + 1/x) + (x)[1 / (x + 1/x)](1 - 1/x^2)
y'/y = ln(x + 1/x) + [x^2/(x^2 + 1)][(x^2 - 1)/x^2]
y'/y = ln(x + 1/x) + (x^2 - 1)/(x^2 + 1)
y' = [(x+1/x)^x][ln(x + 1/x) + (x^2 - 1)/(x^2 + 1)]
c) y = x^x(lnx)
ln y = ln(x^x) + ln(ln x)
ln y = xln x + ln(ln x)
y'/y = ln x + (x)(1/x) + (1/ln x)(1/x)
y'/y = ln x + 1 + 1/(xln x)
y' = x^x(ln x)[ln x + 1 + 1/(xln x)]
y' = x^x(ln x)^2 + x^x(ln x) + x^(x - 1)