Sorry about being unclear, I meant the equation as r(theta) =
And while that is true, why would the chain rule yield that answer. I am asking that you use the chain rule and find the slope and concavity functions and explain why they won't correspond with the concavity of 1/x.
For the polar equation 1/[√(sinθcosθ)]
I found the slope of the graph by using the chain rule and found that dy/dx=−tan(θ)
and the concavity d2y/dx2=2(tanθ)^3/2
This is a pretty messy derivative so I checked it with wolfram alpha and both functions are correct (but feel free to check in case...