This paper explores the application of deep quantum neural networks (DQNN) to financial problems, specifically learning implied volatilities and option prices, and computing Greeks (delta and gamma) analytically. The DQNN architecture, proposed by Beer et al. (2020), generalizes classical deep neural networks to quantum settings, using unitary operations and density matrix propagation. The author encodes financial data (e.g., strike prices, implied volatilities, option prices) into quantum states via a sigmoid-based mapping, enabling the network to learn from training pairs. Numerical experiments demonstrate that DQNN can learn implied volatilities from market data with reasonable accuracy, and increasing the number of qubits in hidden layers yields slight improvements. A key contribution is the analytical computation of Greeks: the paper derives formulas for delta and gamma using the derivative of the input density matrix and the trained DQNN, avoiding numerical differentiation. To incorporate differential learning, a modified cost function is proposed that includes fidelity terms for first and second derivatives, allowing the network to learn both option prices and their sensitivities simultaneously. The results suggest that DQNN is a promising technique for efficient risk management and derivative pricing in finance, leveraging quantum computing's potential for speedup.