If I have u = u(x,y) and let (r, t) be polar coordinates, then(adsbygoogle = window.adsbygoogle || []).push({});

expressing u_x and u_y in terms of u_r and u_t could be

done with a system of linear equations in u_x and u_y?

I get:

u_r = u_x * x_r + u_y * y_r

u_t = u_x * x_t + u_y * y_t

is this the right direction? Because by substitution,

I end up with:

(u_t* x_r - u_r)/(y_t*x_r - y_r) = u_y which

does not seem right, considering:

u_y = u_r * r_y + u_t * t_y

Any insight to the problem is appreciated.

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# Chain rule for partial derivatives

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