## amy0799 one year ago consider the following function. f(x) = sqrt(9-x^2) Find the derivative from the left at x = 3. Find the derivative from the right at x = 3.

find the derivaite, use chain rule, and then plug in 3 for every x

2. amy0799

can you show me how?

3. ChillOut

Let $$u=sqrt(v)$$ and $$v=9-x²$$. What does the chain rule tells you?

4. ChillOut

tell*

5. ChillOut

$$\frac{d}{dx}f(g(x))=f'(g(x))*g'(x))$$

6. Castiel

Make it simpler yourself by writing $(9-x ^{2})^{\frac{ 1 }{ 2 }}$ Now you could use that derivation rule $\frac{ d }{ dx }x ^{n}= nx ^{n-1}$ after that you still have to multiply it with derivation of $\frac{ d }{ dx}(9-x ^{2})$

7. amy0799

would it be 9-2x?

8. Castiel

$\frac{ d }{ dx }(9-x ^{2})$ =$\frac{ d }{dx }9-\frac{ d }{dx }x ^{2}$ Now what is a derivative of a constant number like 9 here?

9. amy0799

0

10. Castiel

that means $\frac{ d }{ dx }(9-x ^{2}) = -2x$

11. amy0799

so then how do i find the derivative from the left and right at x=3?

12. Jhannybean

$\lim_{x\rightarrow 3^{-}} (9-x^2)^{1/2}$$\lim_{x\rightarrow 3^+} (9-x^2)^{1/2}$

13. amy0799

do i just plug in 3 for both equation?

14. amy0799

@ChillOut can you help me

15. triciaal

|dw:1440964454314:dw|

16. amy0799

how do i find the derivative from the left and right at x=3?

17. triciaal

18. triciaal

from the left let x = -3 from the right let x = 3

19. amy0799

20. triciaal

why

21. amy0799

i dont know...

22. triciaal

didn't you put 0?