What is the difference between total derivative and partial derivative?
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Imagine that the price of a new house is a function of two things: the cost of land and the cost of hiring construction workers.
Naively, as the cost of land increases, the final cost of the house will increase by the same amount. That’s the partial derivative.
But what if the labor cost also depends on the cost of land? For example, construction workers need housing themselves; perhaps if their own land costs go up, they will demand higher salaries. In this case, the true relationship between the cost of the house and the cost of land is more complex than just a direct dependency. This relationship is thetotal derivative.
Naively, as the cost of land increases, the final cost of the house will increase by the same amount. That’s the partial derivative.
But what if the labor cost also depends on the cost of land? For example, construction workers need housing themselves; perhaps if their own land costs go up, they will demand higher salaries. In this case, the true relationship between the cost of the house and the cost of land is more complex than just a direct dependency. This relationship is thetotal derivative.
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Partial derivative. In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).
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