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Implicit Differentiation

- Section 2.5

Explicit Differentiation

You have been taught to differentiate functions

in explicit form, meaning y is defined in terms

of x.

Examples

The derivative is

Whenever you can solve for y in terms of x, do so.

Implicit Differentiation

Sometimes, however, y cant be written in terms

of x as demonstrated in the following

We need to differentiate implicitly.

Implicit Differentiation

If variables agree, then use explicit

differentiation.

Example

Simple power rule

Variables agree

If variables do not agree, then use implicit

differentiation.

Chain rule

Variables disagree

Implicit Differentiation

Implicit Differentiation

Example

Implicit Differentiation

Example Determine the slope of the tangent line

to the graph of

at the point

Explicitly

Try the previous example using explicit

differentiation

Implicit Differentiation

Example Find the equation of the tangent line at

(-1,2).

Homework

Section 2.5 page 142 1, 5, 7, 11, 21, 25, 27, 31

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