Final answer:
Implicit differentiation is used to find the derivative of functions implicitly defined by an equation, applying the chain rule and power rule as necessary.
Step-by-step explanation:
Implicit differentiation is a technique used in calculus to find the derivative of a function that is not explicitly solved for one variable in terms of another. It is particularly useful when dealing with equations where direct differentiation is not readily applicable. The process involves differentiating both sides of the equation with respect to x, applying the chain rule for differentiation when necessary.
For example, if we have an equation f(x, y) = 0, and we need to find dy/dx, we differentiate both sides with respect to x, treating y as an implicit function of x. During this process, every time we differentiate a term involving y, we multiply by dy/dx due to the chain rule.
If you encounter additional terms, the power rule of differentiation applies to each term individually, and the total derivative is the sum of the derivatives of the individual terms.