Mar 12, 2013 at 5:24pm UTC
(sqrt(2x + 2h + 1) - sqrt(2x+1) )/h
mult by reciprical
(= 2x+2h+1 - 2x+1)/(sqrt(2x+2h+1) + sqrt(2x+1))
factor h and cancel
[h(2)/[2(sqrt(2x+2h+1) + sqrt(2x+1))]
h goes to 0, cancel h, add sqrt(2x+1) and cancel 2
Mar 12, 2013 at 5:32pm UTC
Wow I forgot to multiply the denominator each time. I feel dumb
Mar 12, 2013 at 5:49pm UTC
Oh man. Derivatives using the limit definition. Those are not fun. I loose myself in them all the time; don't feel dumb, lol.
Mar 12, 2013 at 5:50pm UTC
I got too used to the nice derivative rules heh
Mar 12, 2013 at 5:52pm UTC
I just don't think the limit definition is acceptable. Too much algebra to screw up.
Mar 12, 2013 at 6:07pm UTC
Just wait until you review it in multi-variable.
Mar 12, 2013 at 6:08pm UTC
I've got a couple semesters until that. I don't believe we get into multi-variable calculus until the third semester.
Mar 12, 2013 at 6:09pm UTC
Same here, I'm in calc 3 now.
Mar 12, 2013 at 6:10pm UTC
Ah nice how is it? I think working with 3D shapes sounds interesting.
Mar 12, 2013 at 6:31pm UTC
We actually just talked about implicit differentiation in class today. I assume it's not much different with a third variable involved.
I'll have to check that video out, khan academy is good stuff.