#$&*
course Math 279
been quite a while since i've done this! haha
QA 00My calculus is a bit rusty, its been about a year since my last calculus class. But here goes!
3 sin (4t + 2)
f(x) = 12 cos (4t + 2)
f(x) = -48 sin (4t + 2)
2 cos^2 (3t + 2)
f(x) = 4 cos (3t -1) * -sin (3t -1) (3) = -12sin(3t -1) cos (3t -1)
f(x) = 36 - 172(cos (3t-1))^2
@&
Good, but those (3t - 1) quantities should all be (3t + 2).
*@
A sin (omega * t + phi)
f(x) = A cos (omega * t + phi) (omega)
= omega * A cos (omega * t + phi)
f(x) = omega^2 * A sin (omega * t + phi)
@&
Good, but this last one should be negative. Derivative of cos is - sin.
*@
e^(t^2 -1)
f(x) = e^(t^2 - 1)(2t) = 2te^(t^2-1)
f(x) = 2te^(t^2-1) = 2t(2te^(t^2 -1) + 2(e^(t^2 - 1))
= 4t e^(t^2-1)+ 2 e^(t^2-1)
@&
4t ^2 e^(t^2-1)+ 2 e^(t^2-1) in that last step.
*@
@&
You missed a couple of details, but your overall approach was good throughout. Check my notes.
*@