Implicit differentiation is a mathematical technique used to find the derivative of a function that is not in the form of y = f(x). It is commonly used when a function is defined implicitly, meaning that it is not explicitly written in terms of y.
Implicit differentiation is used when a function cannot be easily solved for y in terms of x. This often occurs when the function is defined implicitly or when it contains both x and y terms.
To perform implicit differentiation, the chain rule is used to find the derivative of the function with respect to x. The y term is treated as a function of x and the derivative is found using the standard rules of differentiation.
Explicit differentiation is used to find the derivative of a function that is in the form of y = f(x), while implicit differentiation is used for functions that cannot be easily solved for y. In explicit differentiation, the derivative is found using the power rule and other standard rules of differentiation.
Implicit differentiation is important because it allows us to find the derivative of functions that cannot be easily solved for y. This is particularly useful in physics and engineering applications where functions are often defined implicitly. It also allows us to find the slope of curves and tangent lines at any point on a graph.