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Differentiation Rules

Differentiation Rules. The PRODUCT Rule: In other words, if y = fg then y’ = fg’ + f’g If y = fgh then y’ = f’gh + fg’h + fgh’. Example. Example. Differentiation Rules. The QUOTIENT Rule: In other words, if , then. Example. Example. Differentiation Rules.

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Differentiation Rules

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  1. Differentiation Rules The PRODUCT Rule: In other words, if y = fg then y’ = fg’ + f’g If y = fgh then y’ = f’gh + fg’h + fgh’

  2. Example

  3. Example

  4. Differentiation Rules The QUOTIENT Rule: In other words, if , then

  5. Example

  6. Example

  7. Differentiation Rules The TRIGONOMIC Functions: These can all be derived from the quotient rule and the derivatives of sine and cosine. You should become familiar with these!

  8. Example The TRIGONOMIC Functions:

  9. Example The TRIGONOMIC Functions: NOTE: Because of trigonometric identities, the derivative of a trigonometric function can take many forms.

  10. High Order Derivatives Just as a velocity function can be obtained by deriving a position function, acceleration can be obtained by deriving a velocity function. Another way of saying this is that the acceleration function can be obtained by deriving the position function twice.

  11. High Order Derivatives

  12. Example

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