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Math Help - Need help

  1. #1
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    Red face Need help

    Q1 - Use chain rule to find df/dx , df/dy
    For f(r,s,v) = r^3 + s + v^2 , where r = xe^y , s = ye^x and v = x^2 y

    Q2 - Spherical coordinates of a point are (4 , π/6 , π/2)

    a - Convert spherical coordinates to rectangular coordinates
    b - Convert spherical coordinates to cylinderical coordinates
    c - Verify your answer by converting back spherical coordinates from anyone of these, that is , either from rectangular or cylinderical coordinates.

    I need detailed answer for Question no. 1 coz i dont know how to start it.. and for Question 2 just hints for that .. Thanks in advance
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  2. #2
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    #1

    Recognize that F(r,s,v) is explicitly dependent upon r,s,v and implicitly dependent upon x and y. Do find df/dx, for example, you need to find df/dr*dr/dx + df/ds*ds/dx + df/dv*dv/dx.

    So, df/dx = 3r^2 * e^y + 1*ye^x + 2v * x

    Did that help at all?
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  3. #3
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    yeah surely it helped.. Thanx alot ..

    and can u help in the 2nd one?
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  4. #4
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    In Q2 plz correct me if am wrong... thanx

    • Assuming the spherical coordinates are (r,theta,phi), rectangular coordinates are:
      x=r sin(theta)cos(phi)=4 * sin(3.14/2) cos(3.14/6)=3.464
      y=r sin(theta)sin(phi)=4 * sin(3.14/2) sin(3.14/6)=2
      z=r cos(theta)=4 * cos(3.14/2)=0

      Cylindrical coordinates are:
      rho = r sin(theta)=4 * sin(3.14/2)=4
      phi = phi=3.14/6
      z= r cos (theta)=4 * cos(3.14/2)=0

      To convert back from cylindrical coordinates
      r=sqrt{rho^2+z^2}=rho=4
      theta=atan2 {rho,z}=atan2(4,0)=3.14/2
      phi=phi=3.14/6
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