 Implicit Functions      Custom Search   IMPLICIT FUNCTIONS In equations containing x and y, separating the variables is not always easy. If we do not solve an equation for y, we call y an implicit function of x. In the equation y is an implicit function of x, and x is also called an implicit funcŁtion of y. If we solve this equation for y, that is then y would be called an explicit function of x. In many cases such a solution would be far too complicated to handle conveniently. When y is given by an equation such as y is an implicit function of x. Whenever we have an equation of this type in which y is an implicit function of x, we can differentiate the function in a straightforward manner. The derivative of each term containing y will be followed by . Refer to Theorem 6. EXAMPLE. Obtain the derivative of SOL UTI0Y- Find the derivative of y2: the derivative of xy2: and the derivative of 2: such that, Solving for we find that and Thus, whenever we differentiate an implicit function, the derivative will usually contain terms in both x and y. PRACTICE PROBLEMS: Find the derivative of the following: ANSWERS:  Integrated Publishing, Inc. - A (SDVOSB) Service Disabled Veteran Owned Small Business