6. If x = eucosv,y = eusinv then
= eusinv then is

6. If x = eucosv,y = eusinv then
= eusinv then is

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1 thought on “6. If x = eucosv,y = eusinv then<br />= eusinv then is<br />дх​”

  1. Answer:

    You’re almost there. First, a miscalculation: your ∂v∂x has the wrong sign. In particular: we indeed have


    It follows that


    which you calculated correctly. However,


    Now, in order to see that JJ′=1, write both Jacobians as a function of the same set of variables. That is, either as a function of x and y or as a function of u and v.

    If we write J′ as a function of u and v, then we find


    In greater detail: we have v(x,y)=tan−1(y/x). We find the derivative of this using the chain rule. Because ddttan−1(t)=11+t2, we have


    To calculate the partial derivative of y/x with respect to x, we use the power rule. In particular:



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