1. Sec 3.5: IMPLICIT DIFFERENTIATION
Example:
In some cases it is possible to solve such an equation for as an explicit function
Example:
In many cases it is difficult (impossible to write y in terms of x)
Fortunately, we don’t need to solve an equation for in terms of in order to find the derivative of . 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’.

2. Sec 3.5: IMPLICIT DIFFERENTIATION
This consists of differentiating both sides of the equation with respect to x and then solving the resulting equation for y’.
Remember:
y is a function of x and using the Chain Rule,
Example:

3. Sec 3.5: IMPLICIT DIFFERENTIATION
This consists of differentiating both sides of the equation with respect to x and then solving the resulting equation for y’.
Remember:
y is a function of x and using the Chain Rule,
Example:

4. Sec 3.5: IMPLICIT DIFFERENTIATION
This consists of differentiating both sides of the equation with respect to x and then solving the resulting equation for y’.
Remember:
y is a function of x and using the Chain Rule,

5. Sec 3.5: IMPLICIT DIFFERENTIATION
Example:
Remember:
In finding y’’ you may use the original equation
fat circle

6. Sec 3.5: IMPLICIT DIFFERENTIATION
DERIVATIVES OF TRIGONOMETRIC FUNCTIONS:
DERIVATIVES OF INVERSE TRIGONOMETRIC FUNCTIONS:

7. differentiate implicitly
Sec 3.5: IMPLICIT DIFFERENTIATION
means
differentiate implicitly

8. Sec 3.5: IMPLICIT DIFFERENTIATION