# help finding derivative

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• November 29th 2008, 03:56 AM
GreenMile
help finding derivative
Hello!

I'm having trouble when i try to derivate this function:

$y=sin^6x+cos^6x+3sin^2xcos^2x$

Any idea?

Thanks.

P.s solution in my book is 0.
• November 29th 2008, 05:08 AM
running-gag
Quote:

Originally Posted by GreenMile
Hello!

I'm having trouble when i try to derivate this function:

$y=sin^6x+cos^6x+3sin^2xcos^2x$

Any idea?

Thanks.

P.s solution in my book is 0.

Hello !
This answer is effectively 0
You can derivate (awful job !)
Or you can see that
$(sin^2x+cos^2x)^3=sin^6x+3sin^4xcos^2x+3sin^2xcos^ 4x+cos^6x$
but
$sin^2x+cos^2x=1$
therefore
$1=sin^6x+3sin^2xcos^2x(sin^2x+cos^2x)+cos^6x$

1=y and then y'=0
• November 29th 2008, 09:59 AM
GreenMile
Sorry how did u get $(sin^2x+cos^2x)^3=sin^6x+3sin^4xcos^2x+3sin^2xcos^ 4x+cos^6x$
• November 29th 2008, 10:21 AM
skeeter
$(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$