2'4 The Chain Rule

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2.4 The Chain Rule

• "I recoil with dismay and horror at this
  lamentable plague of functions which do not have
  derivatives. -- Charles Hermite

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Objectives

• To find derivatives using the chain rule

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Two ways

• Find the derivative of

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A third way

• Chain rule
• y deriv of outside (keep inside same) times
  deriv of inside
• Example

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A fourth way

• Another form of the chain rule
• Example

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Example
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Another example
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What about trig functions?

• Think of u substitution

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You try
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More challenging examples
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Another one

• What rules will we use?

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Yet one more
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Review

• Chain Rule

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2 more examples
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Last one
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Trig Chain Rule

• Deriv of trig (keep angle same) deriv of angle
• Be careful of double chain rule

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Example
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Another example
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Three types