If f and g are functions such that f(g(x))=g(f(x))=x for all x in their domains, and if f(a)=b and f'(a)=c, then g'(b) =?
a) g'(a)=1/c
b) g'(b)=1/c
c) g'(b)=-1/c
d) g'(b)=1/a
e) g'(a)=-1/c
a) g'(a)=1/c
b) g'(b)=1/c
c) g'(b)=-1/c
d) g'(b)=1/a
e) g'(a)=-1/c