Posted by T.Gracken on September 26, 2002 at 17:51:17:
In Reply to: How do i find the derivitave? posted by a.kapoor on September 26, 2002 at 17:13:08:
: I cant seem to find the correct derivitave of this question [(x+2)/(x-2)]^2 do i use the quotient rule or the chain rule? do i use both? if so which one do i use first? Thanks for the help.
Good question. This is a big problem with many students. I will try to make some suggestions while answering.
First, I see "stuff in parenthesis" to a power. So my first thought is 'power rule' (a.k.a. chain rule)
...by the way, I use Dx[A] to mean the derivative of A with respect to x. (i.e. if f(x) = A, then f'(x) = Dx[A] )
so I see: Dx[(x+2)/(x-2)]^2 = 2*[(x+2)/(x-2)]*Dx[(x+2)/(x-2)]
Now, since we want the derivative of a quotient, [(x+2)/(x-2)], use the quotient rule.
so you get Dx[(x+2)/(x-2)] = [(x-2)-(x+2)]/(x-2)2
you finish from there.
However, you can take a product approach...
since [(x+2)/(x-2)]^2 = [(x+2)/(x-2)]*[(x+2)/(x-2)],
you have a product of "stuff in parenthesis"
I'll let you try it from there (if you wish).
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