A partial derivative is a mathematical concept that measures the rate of change of a function with respect to one of its independent variables, while holding all other variables constant. It is represented by the symbol ∂ (pronounced "del").
A partial derivative is calculated by treating all other variables in the function as constants and then taking the derivative of the function with respect to the variable of interest. This process is similar to taking a regular derivative, but only considering one variable at a time.
Taking the partial derivative of y with respect to d means finding the rate of change of the function y with respect to the variable d, while holding all other variables in y constant. In other words, it measures how much y changes when d changes, while everything else stays the same.
The partial derivative is important in science because it allows us to understand how a function changes when we vary one of its independent variables. This is crucial in fields like physics, economics, and engineering, where understanding the relationship between variables is essential.
Δy, or "delta y", represents the change in the output of the function y when the variable d changes. It is used in the formula for the partial derivative to show the change in y over a specific interval of change in d. This helps us to understand the relationship between the variables and how they affect each other.