Posted by dennis on September 27, 2002 at 08:57:52:
In Reply to: How do i find the derivitave? posted by a.kapoor on September 26, 2002 at 17:13:08:
Depending on whether you choose to apply the product or quotient rule first, you may get what appear to be different answers. But they're entirely equivalent.
Here's another approach to your problem.
If y = [(x+2)/(x-2)]^2
then y = [ 1 + 4/(x-2) ]^2
Now you can either:
1) expand the expression and differentiate it:
y = 1 + 8/(x-2) + 16/(x-2)^2
dy/dx = -8/(x-2)^2 - 32(x-2)^3
or
2) differentiate it directly:
y = [ 1 + 4/(x-2) ]^2
dy/dx = 2 [1 + 4/(x-2)] [-4/(x-2)^2]
dy/dx = -8/(x-2)^2 - 32(x-2)^3
It's all the same in the end.