Determining Legendre derivitives

[lycraa]

Determining Legendre derivitives

Homework Statement

if i need to find the derivative of the first Legendre polynomial, P₁(cos$$\Theta$$) can i sub in cos$$\Theta$$ for x in P₁(x) = x?

Homework Equations

The Attempt at a Solution

if that's the case the derivative is just -sin($$\Theta$$), which is easy enough, but if i can't do that substitution then how do i find it? if there is a recurrence relation that I am missing?

 

[lanedance]

that sounds fine to me base don the info you have given, but maybe you should give the whole question - also what you are differentiating with respect to is important, i assume it is theta

basically you are just using chain rule
$$P_1(x(\theta))$$

where
$$x(\theta) = sin(\theta)$$

then
$$\frac{d}{d \theta}P_1(x(\theta)) <br /> = \frac{d P_1(x)}{dx } \frac{d x(\theta)}{d \theta }<br />$$