A partial differential equation derived from the equation z = aeby sinbx will be:

• A. \(\frac{{\partial z}}{{\partial y}} = 2y{\left( {\frac{{\partial z}}{{\partial x}}} \right)^2}\)
• B. \(\left( {1 + \frac{{\partial z}}{{\partial y}}} \right)\frac{{\partial z}}{{\partial x}} = z\)
• C. \(\frac{{{\partial ^2}z}}{{\partial {x^2}}} + \frac{{{\partial ^2}z}}{{\partial {y^2}}} = 0\)
• D. \(2z = x\frac{{\partial z}}{{\partial x}} + y\frac{{\partial z}}{{\partial y}}\)