Implicit differentiation

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In calculus, implicit differentiation is a method for finding the derivative of a function that is defined by an equation rather than by an explicit formula. If an equation such as F ( x , y ) = 0 {\displaystyle F(x,y)=0} defines y {\displaystyle y} as a function of x {\displaystyle x} , at least locally, implicit differentiation treats y {\displaystyle y} as a function y ( x ) {\displaystyle y(x)} and differentiates both sides of the equation with respect to x {\displaystyle x} . The method is an application of the chain rule. Implicit differentiation is useful when solving explicitly for one variable is inconvenient, produces several branches, or...

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