Final answer:
The partial derivative of the expression 5e²xy with respect to x, assuming y is a constant, is 10e²xy.
Step-by-step explanation:
To solve the expression ∂/∂ x 5 e² x y, we must perform a partial derivative with respect to x on the function 5e²xy. Assuming y is a constant with respect to x, the derivative of 5e²xy concerning x would be the derivative of 5 with respect to x (which is 0) plus the product of 5, the derivative of e²x (which is 2e²x since the derivative of e to a power is the same power times e to that power) and y (as a constant).
Therefore, the result is 10e²xy.