what are the first and second derivatives of cos2(theta)?

Answer 1

Let x = theta (for readability's sake on the web)

d/dx cos2x = -sin2x(2)

For trig derivatives, you take the derivative of the function, then the derivative of the parameters.

so d/dx cos2x = -2sin2x

and if we put back in your theta:

d/dx cos2(theta) = -2sin2(theta)

Now for the second derivative:

y" = -2(cos2(theta)(2))
= -4cos2(theta)

Answer 2

Are you asking for the first and second derivative of cos^2(theta)?

Answer 3

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Answer 4

Is that cos^2(theta) or cos(2theta)?

Answer 5

y' = -2sin2theta
y" = -4 cos 2theta

Answer 6

the first is -2sin2theta
the second is -4cos2theata