Double partial derivative with chain rule

This video seeks to explain how to take the second partial derivative of a function f(x,y) where x = rcosθ and y = rsinθ. Unfortunately, my memory card filled up before I finished the problem. After some reflection, I believe it makes more sense to write the final answer in terms of x and y rather than r and θ. With that said, the final answer should be:
f_(xx) * y^2 - 2 f_(xy) * xy + f_(yy) x^2 - f_(x) * x - f_(y) * y

[@surendranpillaibr8588]

This was the video I was looking for thank you very much

[@airpeguiV2]

Thank you very much, you saved my life!!

[@julesshively]

You blue balled me with that last simplification sir

[@ritajagani8443]

Please if you could complete the sum

[@kryptonyeti2599]

Thank you sir

[@nimrakhalid7211]

partial derivative of f w.r.t y, fy , is not just a function of y, why we again consider the fy as a function of x and y and take partial derivative again w.r.t x and y.??

[@scitwi9164]

07:57 and 08:44 - more like a product rule :q

[@brokenangel2513]

thanks

[@ritajagani8443]

I have got it all understood till that part you've taught just complete the remaining pls....

[@BSplitt]

Hi Rita! After looking back on this problem, I feel it would be more concise to write it all out in terms of x's and y's, rather than r's and theta's. So here is the final sum:
f_(xx) * y^2 - 2 f_(xy) * xy + f_(yy) x^2 - f_(x) * x - f_(y) * y
Hopefully that's understandable!

[@BSplitt]

I have posted the final answer in the comments.