proof for product rule(diff) (1 Viewer)

[nonsenseTM]

just curious

 

[SeCKSiiMiNh]

check your syllabus

 

[nonsenseTM]

I know it's obviously not in the syllabus but I'm just interested and don't get this Product rule - Wikipedia, the free encyclopedia (how do they come up with the rectangle?) and the one in cambridge.

 

[untouchablecuz]

maybe this helps

 

[nonsenseTM]

I said I know that one, but thank you anyway cos no body else is replying
lol

 

[shaon0]

I said I know that one, but thank you anyway cos no body else is replying
lol

Quite self explanatory if you look at the diagram.

 

[Trebla]

Using first principles:

 

[cutemouse]

Using first principles:

That's not really a rigorous proof because you're assuming that the functions u and v are continuous...

 

[Trebla]

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.

 

[nonsenseTM]

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