1. Example: Sec 3.7: Implicit Differentiation

2. Example: In some cases it is possible to solve such an equation for as an explicit function In many cases it is difficult (impossible to write y in terms of x) Fortunately, we don’t need to solve an equation for y in terms of x in order to find the derivative of y. Instead we can use the method of implicit differentiation This consists of differentiating both sides of the equation with respect to x and then solving the resulting equation for y’. Sec 3.7: Implicit Differentiation

3. Remember: y is a function of x and using the Chain Rule, This consists of differentiating both sides of the equation with respect to x and then solving the resulting equation for y’. Sec 3.7: Implicit Differentiation Remember: y is a function of x and using the Chain Rule,

4. Remember: y is a function of x and using the Chain Rule, This consists of differentiating both sides of the equation with respect to x and then solving the resulting equation for y’. Example: Sec 3.7: Implicit Differentiation

5. Remember: y is a function of x and using the Chain Rule, This consists of differentiating both sides of the equation with respect to x and then solving the resulting equation for y’. Example: Sec 3.7: Implicit Differentiation

6. Remember: y is a function of x and using the Chain Rule, This consists of differentiating both sides of the equation with respect to x and then solving the resulting equation for y’. Sec 3.7: Implicit Differentiation

7. Remember: In finding y’’ you may use the original equation Example: fat circle Sec 3.7: Implicit Differentiation