___________ of an input is defined as the change in output per unit of change in the input when all other inputs are remain constant.

The correct option is Marginal Product.

In economics, the Marginal Product (MP) of a variable input (such as labor or capital) measures the additional output produced by using one additional unit of that input, while keeping the quantities of all other inputs constant.

Mathematically, if total output is represented by Y and the variable input is represented by X, the Marginal Product is given by the ratio of the change in output to the change in input:
$$MP=\frac{\Delta Y}{\Delta X}$$
This directly matches the definition of "the change in output per unit of change in the input when all other inputs remain constant."

Let's briefly understand why the other options are incorrect:
1. Average Product: This is the total output divided by the total units of the variable input (output per unit of input, rather than the change in output per unit change in input).
2. Total Product: This is the overall amount of output produced using a given combination of inputs.
3. Returns to Scale: This refers to how output changes when all inputs are changed in the same proportion, which contradicts the condition that other inputs remain constant.