Change of derivative variable

  • Thread starter elquin
  • Start date
  • #1
1
0
In spherical coordinates, the operator is defined as

[tex]\frac{\partial^2}{\partial \theta^2}+\cot \theta \frac{\partial}{\partial \theta}[/tex]

Then, substitute

[tex]\mu = \cos \theta[/tex]

and the above is changed to

[tex](1-\mu^2)\frac{d^2}{d \mu^2}-2 \mu \frac{d}{d \mu}[/tex]

I don't know how the last expression is obtained.
Please, help me...
 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
as mu is only a function of theta, could you start with
[tex]
\frac{\partial}{\partial \theta} = \frac{\partial \mu}{\partial \theta} \frac{\partial }{\partial \mu}
[/tex]
 

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