Implicit differentiation is a method used in calculus to find the derivative of a function that is not explicitly written in terms of one variable. It is particularly useful when the function cannot be easily solved for one variable.
Implicit differentiation should be used when the function cannot be easily solved for one variable, or when the given equation contains both the dependent and independent variables. It is also useful when dealing with equations that are not functions, such as circles or ellipses.
To perform implicit differentiation, you first need to identify the function and its variables. Then, you differentiate both sides of the equation with respect to the independent variable, treating the dependent variable as a function of the independent variable. Finally, you solve for the derivative of the dependent variable.
Explicit differentiation involves finding the derivative of a function that is explicitly written in terms of one variable, while implicit differentiation involves finding the derivative of a function that is not explicitly written in terms of one variable. Implicit differentiation is used when the function cannot be easily solved for one variable.
To check your answer for implicit differentiation, you can plug in values for the variables in the original equation and in the derivative you have calculated. If the two values are equal, then your answer is correct. You can also plot the original equation and its derivative on a graph and compare the slopes at different points.