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The Power Rule and other Rules for Differentiation

Learn the power rule, constant rule, constant multiple rule, and sum and difference rules for differentiation. Understand notations for derivatives and simplify the process for finding the derivative of functions.

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The Power Rule and other Rules for Differentiation

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  1. The Power Rule and otherRules for Differentiation Mr. Miehl miehlm@tesd.net

  2. Rules for Differentiation Taking the derivative by using the definition is a lot of work. Perhaps there is an easy way to find the derivative.

  3. Objective • To differentiate functions using the power rule, constant rule, constant multiple rule, and sum and difference rules.

  4. The Derivative is … • Used to find the “slope” of a function at a point. • Used to find the “slope of the tangent line” to the graph of a function at a point. • Used to find the “instantaneous rate of change” of a function at a point. • Computed by finding the limit of the difference quotient as ∆x approaches 0. (Limit Definition)

  5. Notations for the Derivative of a Function “f prime of x” “y prime” “the derivative of y with respect to x” is a noun. is a verb. “Take the derivative with respect to x…”

  6. Rules for Differentiation • Differentiation is the process of computing the derivative of a function. You may be asked to: • Differentiate. • Derive. • Find the derivative of…

  7. Video Clip fromCalculus-Help.com The Power Rule

  8. Rules for Differentiation • Working with the definition of the derivative is important because it helps you really understand what the derivative means.

  9. The Power Rule

  10. The Constant Rule • The derivative of a constant function is zero.

  11. The Constant Multiple Rule • The derivative of a constant times a function is equal to the constant times the derivative of the function.

  12. The Sum and Difference Rules The derivative of a sum is the sum of the derivatives. The derivative of a difference is the difference of the derivatives.

  13. Constant Rule • Find the derivative of:

  14. Power Rule • Differentiate:

  15. Constant Multiple Rule • Find the derivative of:

  16. Constant Multiple Rule • Find the derivative of:

  17. Constant Multiple Rule • Find the derivative of:

  18. Rewriting Before Differentiating

  19. Rewriting Before Differentiating

  20. Rewriting Before Differentiating

  21. Rewriting Before Differentiating

  22. Sum & Difference Rules • Differentiate:

  23. Conclusion • Notations for the derivative: • The derivative of a constant is zero. • To find the derivative of f (x) = xN • Pull a copy of the exponent out in front of the term. • Subtract one from the exponent.

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