Question

cos^2(x^3)
Find the derivative

How is it -6x^2sin(x^3)cos(x^3)
I know you use chain rule but Im confused what else to apply

Answer 1

the derivative of u^2 is 2u u'
the derivative of cos(u) is -sin(u) u'
so, with u=x^3, the derivative of cos^2(x^3), using the power rule as well, is
2cos(3x^2) * -sin(3x^2) * 6x

Answer 2

Yes, I was able to get that arrangement but I couldnt see how it was the same as -6x^2sin(x^3)cos(x^3)

Answer 3

we could fancy that up even a bit more : -6x^2sin(x^3)cos(x^3)
= (-3x^2)(2sin(x^3)cos(x^3))
= (-3x^2)(sin(2x^3) )

..... by using sin(2A) = 2sinAcosA

Answer 4

wow I did mess that up! The derivative is
2cos(x^3) * -sin(x^3) * 3x^2 = -6x^2 cos(x^3) sin(x^3)
or, as Reiny put it.