What is the derivative of y = cos^2(3x)?

5 ⤊

What is the derivative of y = cos^2(3x)?

I reduced it to y= (cos3x)^2 and then worked through it and got that the derivative equals (-6)(cos3x)(sin3x) but im not sure if thats right.
PLEASE SHOW WORK, thanks

2007-10-21 09:00:04 · 3 answers · asked by sam h 1 in Science & Mathematics ➔ Mathematics

3 answers

y = (cos 3 x ) ²
y = 2 (cos 3x) (- 3) (sin 3x)
y = - 6 sin 3x cos 3x
y = (- 3) (2) sin 3x cos 3x
y = (- 3) sin 6x

2007-10-21 11:22:16 · answer #1 · answered by Como 7 · 0⤊ 3⤋

dy/dx = 2*(cos(3x))*d/dx(cos(3x))
= 2*(cos(3x))*(-sin(3x))*d/dx(3x)
= 2*(cos(3x))*(-sin(3x))*3
= -6*cos(3x)sin(3x)

You got it. Two chain rules.

2007-10-21 16:06:26 · answer #2 · answered by Anonymous · 3⤊ 0⤋

y=cos(3x)*cos(3x)
y'=(3*-sin(3x))*cos(3x)+cos(3x)*(3*-sin(3x))
y'=-6*sin(3x)*cos(3x)
yes, that's right

2007-10-21 16:08:04 · answer #3 · answered by キラ 3 · 2⤊ 0⤋