Let be a regular surface and let . then (U,F,V) is a local parametrisation of S at p. Let
Define , with . Then is a basis of the tangent plane
Here , i.e the jacobian then applied to
I am having a lot of trouble trying to show that
I was wondering if anyone could give me some advice on how to think about this, I am very weak in this type of calculus. Thanks very much
Sorry for my mistake. YEs thanks for your reply but I do not know how to apply the chain rule
Lets take to be the first component of .
then I guess I am trying to work out But how do I do this? I cannot use the normal chain rule since there is an intermediate step in , so how do I do this? I have never used a higher dimensional chain rule before. Thanks for any help