y = cos(x) y' = -sin(x)
y = sin(x) y' = cos(x)
the prefix -co in this since means negative
Cos(x) does not turn into Sin(x)
it turns into -Sin(x)
It's crucial that you put a negative in front of -Sin(x) or else your answer is no good. Also if there was a coefficient in front of Cos(x) such as 4Cos(x) the negative would go out in front thus -4Sin(x).
You will see some product rule action in this next one:
we have to do the chain rule on this one.
it might be better to think of cos^2(theta) as (cos(theta))^2. that way, to perform the chain rule, you first have to bring the 2 down and multiply, subtract 1 from the power and leave what's in the brackets, then to complete the chain rule, multiply by the derivative of what's in the brackets.
y = cos^2(theta)
=> y = (cos(theta))^2
=> y' = 2(cos(theta))*(-sin(theta))
=> y' = -2cos(theta)sin(theta)