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I'm working on finding derivatives using the product and quotient rules and the book will

*sometimes*simplify the problem before finding the derivative but

*sometimes*wont and I don't understand why.

For example: The function y = (v

^{3}-2v√v)/v

The book simplifies it to v

^{2}-2v

^{½}and then gets 2v-v

^{-½}as the derivative without even using the product or quotient rules.

Then on this problem: f(x) = x/[x+(c/x)] it doesn't simplify first. I started off by simplifying it as follows:

Original function: f(x) = x/[x+(c/x)]

Making the bottom all one fraction: x/[(x

^{2}+c)/x]

Bottom and top cancel out: 1/(x

^{2}+c).

But using the quotient rule on this gives me an answer of 2x/(x

^{2}+c)

^{2}, which is wrong. The answer is actually 2cx/(x

^{2}+c)

^{2}, which the book gets by using the quotient rule without simplifying first.

When is it okay to simplify before finding the derivative and when isn't it?