Using the limit definition, I just keep getting left with 2, which isn't right. It should
1/sqrt(2x + 1)
Here's what I'm doing:
1 2 3 4
y' = lim x->a (sqrt(2x + 1) - sqrt(2a + 1))/(x - a)) //Limit definition
Multiply by conjugate now... Left with
(2x - 2a)/(x - a)
Factor out 2, the (x - a) terms cancel out. Left with just 2.
Obviously something is going wrong here, and I'm gonna feel stupid when it's pointed out but I'm not seeing it right now -_-
(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
I'ts surprisingly difficult to visualize functions in 3D, making graphing a pain, at least for me. The actual math isn't all that much harder, we are finishing partial derivatives and implicit differentiation which were fairly simple.
If you want to see some interesting stuff check out khan academy's videos on double and triple integrals, we haven't gotten to them yet but I watched the videos and found them very interesting. http://www.khanacademy.org/math/calculus/double_triple_integrals