unj fmipa-fisika

1. Kalkulus I Drs. Tasman Abbas Sesion#15-16 JurusanFisika FakultasMatematikadanIlmuPengetahuanAlam

2. Outline Derivative as a Function 1/10/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 2

3. Derivatives (part 1) © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 3 1/10/2011

4. We write: There are many ways to write the derivative of is called the derivative of at . “The derivative of f with respect to x is …”

5. “the derivative of f with respect to x” “f prime x” or “y prime” “the derivative of y with respect to x” or “dee why dee ecks” “the derivative of f with respect to x” or “dee eff dee ecks” “the derivative of f of x” “dee dee ecks uv eff uv ecks” or

6. Note: dx does not mean d times x ! dy does not mean d times y !

7. does not mean ! does not mean ! Note: (except when it is convenient to think of it as division.) (except when it is convenient to think of it as division.)

8. does not mean times ! Note: (except when it is convenient to treat it that way.)

9. The derivative is the slope of the original function. The derivative is defined at the end points of a function on a closed interval.

11. A function is differentiable if it has a derivative everywhere in its domain. It must be continuous and smooth. Functions on closed intervals must have one-sided derivatives defined at the end points.

12. Thank You 1/10/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 12