A partial derivative is a mathematical concept used in multi-variable calculus to measure the rate of change of a function with respect to one of its variables while keeping the other variables constant.
A partial derivative involves taking the derivative of a function with respect to one variable while holding the other variables constant, whereas a regular derivative involves taking the derivative with respect to a single variable.
When the independent variable is included in the partial derivative, it means that the rate of change of the function is being measured with respect to that particular variable, while keeping all other variables constant.
Partial derivatives are important in many fields of science and engineering, including physics, economics, and engineering. They allow us to analyze the behavior of multi-variable functions and understand how changes in one variable affect the overall function.
One example of a partial derivative with the independent variable is the partial derivative of a function f(x,y,z) with respect to x: ∂f/∂x. This would measure the rate of change of f with respect to x, while holding y and z constant.