Let $V$ be the complex vector space given by $V = \{a\sin(x) + b\cos(x) +cx\sin(x) + dx\cos(x)\ \; | \; a, b, c, d \in \mathbb{C}\}$
Let $D: V \rightarrow V$ be the linear map given by $D(f) = f'$.
I need to work out the characteristic equation and complex eigenvalues of D and $m_D x$.
I thought the first step would be to calculate the derivative but I don't know where to go from here?