  In this paper we recover Bousfield's computation of $\nu_1$-periodic homotopy
groups of simply connected, finite $H$-spaces from \cite{Bou99} using the
techniques of Goodwillie calculus. This is done through first computing
Andr\'{e}-Quillen cohomology over the monad $\mathbb{T}$ that encodes the power
operations of complex $K$-theory. Then lifting this computation to computing
$K$-theory of topological Andr\'{e}-Quillen cohomology, and then using results
of Behrens and Rezk relating it back to the Bousfield-Kuhn functor. The fact
that we recovers the result of Bousfield allows us to conclude $\nu_1$-periodic
Goodwillie tower for simply connected, finite $H$-spaces converges.
