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Differentiating “Combined” Functions ---Part I

Learn how to compute the derivatives of algebraic combinations of functions by utilizing the derivatives of simple functions. Explore the derivative of a constant times a function, the derivative of the sum of two functions, and the derivative of the difference of two functions.

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Differentiating “Combined” Functions ---Part I

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  1. Differentiating “Combined” Functions ---Part I Constant Multiples, Sums and Differences

  2. Algebraic Combinations • We have seen that it is fairly easy to compute the derivative of a “simple” function using the definition of the derivative. • More complicated functions can be difficult or impossible to differentiate using this method. • So we ask . . . If we know the derivatives of two fairly simple functions, can we deduce the derivative of some algebraic combination (e.g. the sum or difference) of these functions without going back to the difference quotient? Yes!

  3. The Derivative of a constant times a function Can we do this?

  4. What does this mean?

  5. The Derivative of the Sum of Two Functions Can we do this?

  6. The Derivative of the Difference of Two Functions Now you do this!

  7. The Derivative of the Difference of Two Functions

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