Assume that the equation exyz sin x y z implicitly defines z as a function of x y We will find using two methods z x a Go through and implicitly take partial derivatives with respect to x on both sides of the given equation treating z as a function of x and treating y as constant and remembering to use the chain rule when necessary Then solve for This is the method you learned in Calc I x b i Ignore the above equation for a moment and consider the general case where some equation F x y z 0 implicitly defines z as a function of x y Use the multivariable chain rule to find a general formula for x z ii Now use the formula you found to find az for the above example x