Unformatted text preview: y represents a function of x . In other words, y can be defined implicitly as a function of x . So when we take the derivative of y , we must apply the chain rule. term derivative 5x 3 15x 2 3y 2 9y dy dx or 9yy’ (since y represents some function in terms of x) Implicit differentiation avoids solving complicated equations explicitly for y . However, the derivative formulas obtained by implicit differentiation usually involve both x and y , not just x as with ordinary functions. Try exercises 2, 10, 20, 22, 24, 26, 46, 52 on pages 213214 in your text....
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 Spring '11
 Teague
 Calculus, Addition, Equations, Derivative, Implicit Differentiation, Expression, explicit form

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