1. ## 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

2. #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?

3. yeah surely it helped.. Thanx alot ..

and can u help in the 2nd one?

4. 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