Implicit Differentiation

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Implicit Differentiation

• Section 2.5

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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.
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Implicit Differentiation
Sometimes, however, y cant be written in terms
of x as demonstrated in the following
We need to differentiate implicitly.
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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
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Implicit Differentiation
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Implicit Differentiation
Example
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Implicit Differentiation
Example Determine the slope of the tangent line
to the graph of
at the point
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Explicitly
Try the previous example using explicit
differentiation
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Implicit Differentiation
Example Find the equation of the tangent line at
(-1,2).
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Homework
Section 2.5 page 142 1, 5, 7, 11, 21, 25, 27, 31