Partial derivative of summation and tranpose

Question

I am stuck with the partial derivative of summation of a variable and want to know is there any partial derivative that calculates to its transpose? I am attaching figures for reference. Please help. In this expression, i want to calculate the partial derivative of this equation w.r.t $w_k$:$$\sum_{k=1}^nw_k(n)\mathbf{\phi}\{\mathbf{x}(n),\,\mathbf{c}_k(n),\,\sigma_k(n)\}$$ And can any partial derivative calculates to the tranpose which give this is as the answer?$$\mathbf{\Psi}(n)=[\phi\{\mathbf{x}(n,\,\mathbf{c}_1,\,\sigma_1)\},\,\phi\{\mathbf{x}(n,\,\mathbf{c}_2,\,\sigma_2)\},\,\cdots,\,\phi\{\mathbf{x}(n,\,\mathbf{c}_1,\,\sigma_1)\}]^T$$