# Math Help - easy product rule differentiation

1. ## easy product rule differentiation

just need a check to make sure i'm doing this right.

its just a derivative: cos(cosx)*(-sinx)

so i would use the product rule.

is this correct:
-sin(cosx)(-sinx)*(-sinx) + cos(cosx)*(-cosx)

thanks for checking.
if its not correct please fix it, and if it is, maybe help me clean up the negative signs.

thanks.

2. ## Differentiating

Hello rcmango
Originally Posted by rcmango
just need a check to make sure i'm doing this right.

its just a derivative: cos(cosx)*(-sinx)

so i would use the product rule.

is this correct:
-sin(cosx)(-sinx)*(-sinx) + cos(cosx)*(-cosx)

thanks for checking.
if its not correct please fix it, and if it is, maybe help me clean up the negative signs.

thanks.
Your working is fine. You can tidy it up a bit to get:

$-\sin(\cos x)\sin^2x-\cos(\cos x)\cos x$

Otherwise there's not much else that will simplify.