Transforming Derivative Operator in Spherical Coordinates with Substitution

[elquin]

In spherical coordinates, the operator is defined as

$$\frac{\partial^2}{\partial \theta^2}+\cot \theta \frac{\partial}{\partial \theta}$$

Then, substitute

$$\mu = \cos \theta$$

and the above is changed to

$$(1-\mu^2)\frac{d^2}{d \mu^2}-2 \mu \frac{d}{d \mu}$$

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

 

[lanedance]

as mu is only a function of theta, could you start with
$$\frac{\partial}{\partial \theta} = \frac{\partial \mu}{\partial \theta} \frac{\partial }{\partial \mu}$$