higherorderderivatives-200920041748 (1).pptx

derivatives

1. Chapter 4 Class: XII

2. H igher order derivatives

3. Basic Calculus What you need to know already: Basic Differentiation Rules What you can learn here: How to repeat the process of differentiation to obtain derivatives of derivatives 3

4. notice! Do you remember the different notations for derivatives? 4

5. 5 Well these are the same notations for higher power derivatives! Any guesses on what each means?

6. 6 And to find them you just take the derivative again...and again…if necessary! For example to get from f’’(x) to f’’’(x) you just take the derivative of f’’(x). And to get from f’(x) to f (4) (x) you would just take the derivative of f’(x) three times.

7. 1. 7 Find the second derivative of f(x) = x 4 – 2x 3 [Sol]

8. 8 2. If f(x) = x 3 − 6x 5 , then [Sol] f (1) (x) = 3x 2 − 30x 4 f (2) (x) = 6x − 120x 3 f (3) (x) = 6 − 360x 2 f (4) (x) = −720x f (5) (x) = −720 f (6) (x) =

9. 9

10. summary! Higher derivatives are obtained by successively computing the derivative of a lower order derivative. The order of a derivative refers to how many times differentiation has been performed, starting from the original function. 10

11. C ommon errors to avoid! When looking for a pattern for the higher derivatives of a function, don’t stop too soon: you may need at least 5-6 derivatives before it becomes clear. 11

12. thanks! 12