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?

3. differentiable Note: We are going to assume that all of the functions we talk about in this PowerPoint presentation are differentiable.

4. THE DERIVATIVE OF A CONSTANT TIMES A FUNCTION Can we do this? Why?

5. WHAT DOES THIS MEAN?

6. THE DERIVATIVE OF THE SUM OF TWO FUNCTIONS Can we do this?

7. THE DERIVATIVE OF THE DIFFERENCE OF TWO FUNCTIONS