- #1
limitkiller
- 80
- 0
that is too sad
it have been 2 days and i coudnt find out where do i make mistake.
i wanted to prove:" (f(x)*g(x))'= g(x)*f(x)'+ g(x)'*f(x)". so:
(f(x)*g(x))'= lim h→0 ((f(x+h)*g(x+h)-f(x)*g(x))/h)
=lim h→0 ((f(x+h)*g(x+h))/h) - lim h→0 (f(x)*g(x))/h)
=[lim h→0 ((f(x+h))/h)*lim h→0 (g(x+h))] - [ lim h→0 ((f(x))/h) * lim h→0 (g(x))]
=[lim h→0 ((f(x+h))/h)* g(x)] - [ lim h→0 ((f(x))/h) * (g(x)]
= g(x)*[lim h→0 ((f(x+h))/h) - lim h→0 ((f(x))/h)]
= g(x)*[lim h→0 ((f(x+h)-f(x))/h)]
= g(x)*f(x)'
then (f(x)*g(x))'= g(x)*f(x)' !(?)!
it have been 2 days and i coudnt find out where do i make mistake.
i wanted to prove:" (f(x)*g(x))'= g(x)*f(x)'+ g(x)'*f(x)". so:
(f(x)*g(x))'= lim h→0 ((f(x+h)*g(x+h)-f(x)*g(x))/h)
=lim h→0 ((f(x+h)*g(x+h))/h) - lim h→0 (f(x)*g(x))/h)
=[lim h→0 ((f(x+h))/h)*lim h→0 (g(x+h))] - [ lim h→0 ((f(x))/h) * lim h→0 (g(x))]
=[lim h→0 ((f(x+h))/h)* g(x)] - [ lim h→0 ((f(x))/h) * (g(x)]
= g(x)*[lim h→0 ((f(x+h))/h) - lim h→0 ((f(x))/h)]
= g(x)*[lim h→0 ((f(x+h)-f(x))/h)]
= g(x)*f(x)'
then (f(x)*g(x))'= g(x)*f(x)' !(?)!