The partial derivative of $y$ with respect to $x$ is given by:
\[\frac{\partial y}{\partial x} = A \cos(px+a) \cos(qt+b) \cdot p\]
The partial derivative of $y$ with respect to $t$ is given by:
\[\frac{\partial y}{\partial t} = -A \sin(px+a) \sin(qt+b) \cdot
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