- #1
daster
Say we have two functions of x, v and y, such that v=x+y. How can I find v'?
Implicit differentiation is a mathematical technique used to find the derivative of a function that is given implicitly, meaning the dependent and independent variables are not explicitly defined in the equation. In other words, the equation is not in the form of y = f(x).
Explicit differentiation is used to find the derivative of a function that is given explicitly, meaning the dependent and independent variables are clearly defined in the equation. Implicit differentiation, on the other hand, is used for equations that are not explicitly defined.
The process of implicit differentiation involves taking the derivative of both sides of the equation with respect to the independent variable. Then, use the rules of differentiation to solve for the derivative of the dependent variable. The result will be in terms of both the dependent and independent variables.
Implicit differentiation is used when the equation cannot be solved for the dependent variable explicitly and when the derivative of the dependent variable is needed.
Implicit differentiation is commonly used in physics, engineering, and economics to solve problems involving rates of change and optimization. It can also be used in curve fitting and data analysis.