3.6 Implicit Differentiation

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3.6 Implicit Differentiation

• And Rational Exponents

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Rational Exponents are easy!

• These problems will have exponents that arent
  integers they will most likely be fractions.
• Hmmm how could an exponent be a fraction??
• Thats right! A radical!!
• It doesnt matter. You will still use the
  generalized power rule

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Examples

1. Find if
2. Find if

Functions do NOT need to be rationalized only
numbers need to be rationalized.
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Implicit Differentiation

• This process is used when y cannot be isolated.
  We will look at a problem where y CAN be isolated
  to understand the idea, but in many problems y
  will be mixed in as a product or a quotient.
• We will be treating y as a differentiable
  functions.

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Lets try this one
The derivative of y in terms of x has to have
that extra symbol because y is not x
Same thing right?
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What does this mean?

• WHENEVER you have to take a derivative of
• y, tack on . No kidding. ?
• Then, isolate . There might be y in your
• answer it also might be easy to sub back in
  y.
• Lets see an example or two.

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Examples

• 3. Find if
• Find if
• Find if (hint
  continue 4)

Leave y in the answer.
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Examples

• 6. Find the slope at (-1, 1) for