find dy/dx of

y= (cosx/x) + (x/cosx)

i got up to

((xsinx-cosx)/x^2 ) + ((cosx+sinx)/cosx^2))

and i don't know how to simplify it.

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- Oct 8th 2007, 11:56 AMrmnderivatives of trigonometric functions
find dy/dx of

y= (cosx/x) + (x/cosx)

i got up to

((xsinx-cosx)/x^2 ) + ((cosx+sinx)/cosx^2))

and i don't know how to simplify it. - Oct 8th 2007, 12:08 PMJhevon
- Oct 8th 2007, 12:55 PMrmn
ok so I now have

((xcosx)(-sinx^2 + 2x) - (cosx^2+x^2)(x)(-sinx)+cosx) / (xcosx)^2

i'm confused of how to simplify.. like how do you multiply xcosx with stuff? - Oct 8th 2007, 01:07 PMJhevon
- Oct 8th 2007, 01:31 PMJhevon
after trying your way and my way, i found that the problem is generally easier to do your way. however, i do not see a worth-while way to simplify anything, so just leave the answer as:

or if you feel like, you can combine these fractions to get:

but i don't see any motivation for doing even that