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We want to find the first partial derivatives of the function, f of xy, is equal to 2x, e to the xy squared, minus the tangent of 2x plus y.
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This question is challenging our ability to take partial derivatives using single variable calculus methods.
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So, the first partial derivatives we're looking for are dfdx and dfdy.
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To obtain both, we use the standard differentiation techniques we learned in single variable calculus, where, for dfdx, we differentiate with respect to x, but take y as a constant, and for dfdy, we take x as a constant.
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So we can go and proceed...