We present TensorGrad, a differentiable tensor-network framework for variational optimization of quantum many-body ground states. The method combines finite-difference and autodifferenti- ation backends to optimize matrix-product-state (MPS) parameters using gradient descent. Ap- plied to benchmark models such as the Transverse-Field Ising Model (TFIM) and the Heisenberg spin chain, TensorGrad efficiently converges to low-energy configurations using a minimal ansatz. Furthermore, an additional two-body entangler circuit introduces controlled quantum correlations, enabling non-trivial reductions in ground-state energy and measurable increases in entanglement entropy. The framework also computes entanglement spectra and von Neumann entropy profiles, offering an accessible platform to study the interplay between variational optimization and entan- glement in differentiable physics.