Let D = {z ∈ C : |z| < 1} be the open unit disk in the complex plane C. By H(D), denote the space of all holomorphic functions on D. For an analytic self map φ on D and u, v ∈ H(D), we have a product type operator T u,v,φ defined by T u,v,φ f (z) = u(z) f (φ(z)) + v(z) f ′ (φ(z)), f ∈ H(D), z ∈ D, This operator is basically a combination of three other operators namely composition operator, multiplication operator and differentiation operator. We study the boundedness and compactness of this operator from Dirichlet-type spaces to Zygmund-type spaces.