- #1
candynrg
- 5
- 0
Use Implicit Differenciation to find y' f tan(x^2 + y^2) = sec(xy)
Implicit differentiation is a mathematical technique used to find the derivative of a function that is defined implicitly rather than explicitly. This means that the function is not expressed in terms of a single dependent variable, but rather as a relationship between two or more variables.
Implicit differentiation is used when a function cannot be easily solved for the dependent variable in terms of the independent variable. This may be due to the presence of multiple variables or complex relationships between variables.
Explicit differentiation is used to find the derivative of a function that is expressed explicitly in terms of the independent variable. Implicit differentiation, on the other hand, is used to find the derivative of a function that is defined implicitly in terms of multiple variables.
The process for implicit differentiation involves treating the dependent variable as a function of the independent variable and using the chain rule to find the derivative. This involves taking the derivative of each term in the function and then solving for the derivative of the dependent variable.
Implicit differentiation is used in various fields, including physics, engineering, and economics. It can be used to analyze the relationships between multiple variables and to find rates of change in complex systems. For example, it can be used to find the rate at which a population is growing or to determine the acceleration of an object in motion.