Lauren1234

How does one show the below matrix is a linear transformations I know I need to multiply something by (0,1) and (1,0)

Sorry it should be Let A={e^xsin(x),e^xcos(x),sin(x),cos(x)}

Let A={ex,sin(x),excos(x),sin(x),cos(x)} and let V be the subspace of C(R) equal to span(A). Define T:V→V,f↦df/dx. How do I prove that T is a linear transformation? (I can do this with numbers but the trig is throwing me).