• Best of luck to the class of 2024 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here
  • YOU can help the next generation of students in the community!
    Share your trial papers and notes on our Notes & Resources page

proof for product rule(diff) (1 Viewer)

nonsenseTM

Member
Joined
May 29, 2009
Messages
151
Gender
Male
HSC
2010
I said I know that one, but thank you anyway cos no body else is replying
lol
 

Trebla

Administrator
Administrator
Joined
Feb 16, 2005
Messages
8,328
Gender
Male
HSC
2006
Using first principles:

 

Trebla

Administrator
Administrator
Joined
Feb 16, 2005
Messages
8,328
Gender
Male
HSC
2006
That's not really a rigorous proof because you're assuming that the functions u and v are continuous...
The continuity is sort of implied with the fact that the derivative exists for both functions (a requirement for the product rule).

If the derivative exists at a certain point, that function must clearly be continuous at that point. If at least one of the functions wasn't continuous at a given point then obviously differentiation by the product rule is not well defined for that point.

There is no such 'proof' that weakens the assumptions of continuity or differentiability simply because the derivative wouldn't be defined at discontunities and non-differentiable points hence it obvious that you can't prove the product rule under such circumstances.
 
Last edited:

nonsenseTM

Member
Joined
May 29, 2009
Messages
151
Gender
Male
HSC
2010
The continuity is sort of implied with the fact that the derivative exists for both functions (a requirement for the product rule).

If the derivative exists at a certain point, that function must clearly be continuous at that point. If at least one of the functions wasn't continuous at a given point then obviously differentiation by the product rule is not well defined for that point.

There is no such 'proof' that weakens the assumptions of continuity or differentiability simply because the derivative wouldn't be defined at discontunities and non-differentiable points hence it obvious that you can't prove the product rule under such circumstances.
thanks a lot
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top