The first partial derivative with respect to $x$ is given by:
$$f_{x}=\frac{\partial f}{\partial x}=3x^{2}y^{5}+8x^{3}y$$
And the first partial derivative with respect to $y$ is given by:
$$f_{y}=\frac{\partial f}{\partial y}=5x^{3}y^{4}+2x^{4}$$
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