Sec 3.5: IMPLICIT DIFFERENTIATION

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Presentation transcript:

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’.

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:

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:

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,

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

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

differentiate implicitly Sec 3.5: IMPLICIT DIFFERENTIATION means differentiate implicitly

Sec 3.5: IMPLICIT DIFFERENTIATION