Thread: derivatives 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.

Originally Posted by rmn

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.

perhaps it would be easier to simplify if you had combined the fractions first.

note that:

Now, perform the quotient rule on that.

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?

Originally Posted by rmn

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?

that derivative is incorrect. you need the chain rule to derive things like

this is my 42th post!!!!

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