Question

What is the slope of the rose r=2cos2theta at the point theta = pi

Answer 1

you got the formula for the derivative?

Answer 2

Or can you make it into something you can find the derivative of?

Answer 3

if not we can recreate it fast, since
\[y=r\sin(\theta)\] and \[x=r\cos(\theta)\] and \[\frac{dy}{dx}=\frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}\]

Answer 4

I don't have the formula for the derivative.

Answer 5

product rule
\[\frac{dy}{d\theta}=r'\sin(\theta)+r\cos(\theta)\]
\[\frac{dx}{d\theta}=r'\cos(\theta)-r\sin(\theta)\]

Answer 6

and so
\[\frac{dy}{dx}\] is the ratio of those two

Answer 7

Thank you.