Need some help with Log Differentiation?

Question

(ln(x+1))^(cosx)

ln(x^2+y^2)

x^y=y^x

Answer 1

1) f(x) =[ln(1+x)]^cos x
ln f= cos (x) * ln [ln(1+x)]
f´/f = -sin(x) *ln[ln(1+x)]+ cos(x) * 1/ln(1+x) * 1/(1+x)
To get f´multiply the right side by f(x)
2)You must write it = to something

3) y*ln x= x*ln y
y´*lnx+y/x= ln y +x*y´/y
y´( ln x-x/y)= ln y-y/x
y´= (ln y-y/x)/(ln x-x/y)