Trig identities and differentiation: I differentiated (cos(3x))^2 and got -6cos(3x)sin(3x) but answer key says -3cos(6x)

johnflynn

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I have to differentiate (cos (3x))^2 which I did and got -6cos(3x)sin(3x), but the answer says it's -3cos(6x).....please help! Thanks
 
If you think that your answer is correct, then use some type of software to verify that [-6cos(3x)sin(3x)] - [-3cos(6x)] = 0.
The fact that the angle doubled, by going from 3x to 6x, you should think double angle formula.
 
Just to clarify, everyone is now agreed that the book's answer is wrong, yes?

The correct answer should be -3sin(6x) not -3cos(6x)

(because \(\displaystyle \tiny{\frac{\mathrm{d}}{\mathrm{d}x}}\footnotesize (cos(3x))^2=-6cos(3x)sin(3x)=-3sin(6x)\))
 
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