IMPLIED DERIVATION | DERIVATIVE
IMPLICIT DIFFERENTIATION (OR DERIVATION) | DERIVATIVE
Implicit Derivation
IMPLICIT DIFFERENTIATION (OR DERIVATION) | DERIVATIVE
Implicit Differentiation
Whenever we have a function written in the form y = f(x), we say that y is an explicit function of x, because we can isolate the dependent variable on one side and the function expression on the other. However, this is not always possible or convenient, and if it does, we say that y is an implicit function of x. Let's look, for example, at the equation y = 2x^2 – 3. We can see that y is an explicit function of x, since we can write y = f (x), where f (x) = 2x^2 – 3. However, the equation 4x^2 – 2y = 6 defines the same function, since isolating y we obtain y = 2x^2 – 3. When written in the form 4x^2 – 2y = 6, we say that y is an implicit function of x.