f'(x)
=lim(y->0) [f(x+y) -f(x)]/y
=lim(y->0) [f(x)f(y) -f(x)]/y
=lim(y->0) f(x)[f(y) -1]/y
=lim(y->0) f(x)[{1+yf(y)} -1]/y
=lim(y->0) f(x)*[f(y)]/y
=f(x)
f'(x)
=lim(y->0) [f(x+y) -f(x)]/y
=lim(y->0) [f(x)f(y) -f(x)]/y
=lim(y->0) f(x)[f(y) -1]/y
=lim(y->0) f(x)[{1+yf(y)} -1]/y
=lim(y->0) f(x)*[f(y)]/y
=f(x)