What is partial derivative?
A mathematical concept used to measure the rate of change of a function with respect to one of its variables while keeping the other variables constant
partial derivative explained in plain English
In calculus, a partial derivative is a way to understand how a function changes when one of its inputs changes, while the other inputs remain the same. It's like looking at how a specific knob affects a machine, while keeping all the other knobs in the same position
Analogy
Imagine you're adjusting the temperature and humidity in a greenhouse to grow plants. The partial derivative of plant growth with respect to temperature would tell you how much the plant growth changes when you adjust the temperature, while keeping the humidity constant
Example
In economics, partial derivatives can be used to understand how a change in the price of a product affects its demand, while keeping other factors like advertising and seasonality constant
How is partial derivative used?
Common misconceptions about partial derivative
A common misconception is that partial derivatives are only used in calculus, when in fact they have many practical applications in various fields
History
The concept of partial derivatives was first introduced by the French mathematician Alexis Clairaut in the 18th century, and later developed by other mathematicians like Leonhard Euler and Joseph-Louis Lagrange
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