JonF said:How do you not know how to get it? You just said how! Use the quotient rule on the RHS.
Implicit differentiation is a mathematical technique used to differentiate a function that is defined implicitly by an equation. This means that the equation does not explicitly express one variable in terms of the other, making it difficult to differentiate using traditional methods.
Explicit differentiation involves differentiating a function that is expressed explicitly in terms of one variable. Implicit differentiation, on the other hand, involves differentiating a function that is defined implicitly by an equation, where one variable is not explicitly expressed in terms of the other.
Implicit differentiation is useful when differentiating functions that cannot be expressed explicitly in terms of one variable, such as curves or surfaces defined by implicit equations. It is also useful in cases where the derivative of a function is needed, but the function is too complex to differentiate using traditional methods.
The process for implicit differentiation involves treating the dependent variable as a function of the independent variable, and then using the chain rule to differentiate both sides of the equation with respect to the independent variable. The resulting equation can then be solved for the derivative of the dependent variable.
One common mistake when using implicit differentiation is forgetting to apply the chain rule when differentiating the dependent variable. It is also important to correctly identify the dependent and independent variables in the equation. Additionally, care must be taken when solving for the derivative, as it may involve both the dependent and independent variables.