If $P_n(1)=1$ calculate $P'_n(1)$ in Legendre polynomials $P_n(x)$ is in $[-1,1]$ and $P_n(1)=1$ .The problem is getting $P'_n(1)$.
On Wikipedia it says that it is $\frac{n(n+1)}2$.
I derive the problem showed here
How could I prove that $P_n (1)=1=-1$ for the Legendre polynomials?
in order to get P'(n) but it didn't helped so much.

It follows by induction from the recurrence
$$
 (n+1) P_{n+1}(x) = (2n+1) x P_n(x) - n P_{n-1}(x)
$$
Just differentiate both sides and use that $P_n(1)=1$. 
