AP Calculus BC 10.15: Power Series Operations

The Taylor series for a function f about x=4 is given by

$\sum_{n=1}^{\infty} \frac{(x-4)^{n+1}}{(n+1) 3^{n}}=\frac{(x-4)^{2}}{2 \cdot 3}+\frac{(x-4)^{3}}{3 \cdot 3^{2}}+\frac{(x-4)^{4}}{4 \cdot 3^{3}}+\cdots+\frac{(x-4)^{n+1}}{(n+1) 3^{n}}+\cdots$ and converges to f(x) on

its interval of convergence.

Find the first three nonzero terms and the general term of the Taylor series for $f^{\prime}$, the

derivative of f, about x=4.