What is partial derivative of an integral?

The partial derivative of an integral is called the partial derivative of a function with respect to one of its variables, while holding the other variables constant. The partial derivative of an integral is written as:

∂/∂x ∫f(x,y)dy

This means that we take the derivative of the integral with respect to x, while treating y as a constant. The process for finding the partial derivative of an integral is similar to finding the derivative of a regular function, and involves applying the derivative rules to the integrand before integrating.

The partial derivative of an integral is useful in many fields of mathematics, including calculus, differential equations, and mathematical modeling. It allows us to analyze the behavior of a function as one variable changes, while holding the other variables constant. This is particularly important in physics and engineering, where we often deal with complex systems of equations that depend on multiple variables.

Overall, the partial derivative of an integral provides a powerful tool for understanding the behavior of functions with multiple variables, and is an essential concept in many areas of mathematics and science.