1. ## [SOLVED] Derivative problem

ok, i was doing my hw and i just do not have a clue how to solve this.
the problem is:
(2x^3-x)cos(1-x^2)

and this is what i got or attempted so far. i'm not even sure if this is the right way. can somebody tell me where i went wrong?

[d/dx(2x^3-x)cos)1-x^2) x (2x^3-x)[d/dx(cos(1-x^2))]
=(6x^2-1)cos(1-x^2) x 2x(2x^3-x)sin(1-x^2)

thanks much!

2. Originally Posted by katieeej
ok, i was doing my hw and i just do not have a clue how to solve this.
the problem is:
(2x^3-x)cos(1-x^2)

and this is what i got or attempted so far. i'm not even sure if this is the right way. can somebody tell me where i went wrong?

[d/dx(2x^3-x)cos)1-x^2) x (2x^3-x)[d/dx(cos(1-x^2))]
=(6x^2-1)cos(1-x^2) x 2x(2x^3-x)sin(1-x^2)

thanks much!
you have to use the product rule, look it up. also note that you need the chain rule to differentiate $\displaystyle \cos (1 - x^2)$, so look that up as well

$\displaystyle y = (2x^3 - x) \cos (1 - x^2)$

$\displaystyle \Rightarrow y' = (6x^2 - 1) \cos (1 - x^2) - 2x(2x^3 - x) \sin (1 - x^2)$