Word Count : 347

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The given function is: \[ f(x, y) = x^2 \sin(y) + y^2 \cos(x) \] ### First-order partial derivatives: 1. Partial derivative with respect to \( x \): \[ \frac{\partial f}{\partial x} = \frac{\partial}{\partial x} \left( x^2 \sin(y) + y^2 \cos(x) \right) \] Using the product rule and simplifying: \[ \frac{\partial f}{\partial x} = 2x \sin(y) - y^2 \sin(x) \] 2. Partial derivative with respect to \( y \): \[ \frac{\partial f}{\partial y} = \frac{\partial}{\partial y} \left( x^2 \sin(y) + y^2 \cos(x) \right) \] Using the product _________ _____ _____ ___ __________ _______ ___.
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