- #1
Maxwell
- 513
- 0
Here is the problem:
Determine the orthogonal trajectories of the given family of curves.
[tex] y = \sqrt{2\ln{|x|}+C} [/tex]
This is what I've done so far:
[tex] y = (2\ln{|x|}+C)^\frac{-1}{2} [/tex]
[tex] y' = -1/2(2\ln{|x|+C)(2/x) [/tex]
Now I understand to find the orthogonal lines I need to divide -1 by whatever I get, the problem is, I can't simplify this derivative.
I've messed around with it a bit, and I have this:
[tex] -(2\ln{|x|}+C)/x [/tex]
How else can I simplify this?
Thanks.
Determine the orthogonal trajectories of the given family of curves.
[tex] y = \sqrt{2\ln{|x|}+C} [/tex]
This is what I've done so far:
[tex] y = (2\ln{|x|}+C)^\frac{-1}{2} [/tex]
[tex] y' = -1/2(2\ln{|x|+C)(2/x) [/tex]
Now I understand to find the orthogonal lines I need to divide -1 by whatever I get, the problem is, I can't simplify this derivative.
I've messed around with it a bit, and I have this:
[tex] -(2\ln{|x|}+C)/x [/tex]
How else can I simplify this?
Thanks.