## anonymous 3 years ago Calculate the derivative of the function. Use Chain Rule g(z) = (z^2/7+z)^2

1. anonymous

Can you set it up?

2. anonymous

im guessing its 2(z^2) x 2(7)

3. anonymous

|dw:1351750568965:dw|Is this the function?

4. anonymous

@baldymcgee6 yes, and @sirm3d no the Z is squared

5. anonymous

sorry i mistyped

6. anonymous

yea i just have a hard time with this one. maybe because its a different format

7. anonymous

the first part is differentiating the square

8. anonymous

$2\left( \frac{ z^{2} }{ 7+z } \right)$

9. anonymous

There is an easier method if you want..

10. anonymous

|dw:1351750799134:dw|Just use the power rule and chain rule throughout, no need for quotient rule.

11. anonymous

the second part is where the chain rule is used. Get the derivative of $\frac{ z^{2} }{ 7+z }$ by the quotient rule for differentiation

12. anonymous

|dw:1351750960037:dw|

13. anonymous

You will actually need the product rule because the co-efficient is a variable.

14. anonymous

@sirm3d so the derivative would be 2x/7 ?and @baldymcgee6 so the previous equation you typed is the product rule? or chain?

15. anonymous

nope. the quotient rule on $\frac{ z^{2} }{ 7+z }$ will produce $\frac{ \left( 7+z \right)\left( 2z \right)-\left( z^{2}\left( 1 \right) \right) }{ \left( 7+z \right)^{2} }$

16. anonymous

|dw:1351751195729:dw|

17. anonymous

@baldymcgee6 quick question. where did u get (-1) in the very first step in the equation

18. anonymous

|dw:1351751807412:dw|

19. anonymous

yes

20. anonymous

|dw:1351751909040:dw|

21. anonymous

also the second step the last part of the equation is cut off -2(7+z....

22. anonymous

sorry, my drawings keep getting cut off for some reason. -2(7+z)^-3 Just using power rule there.

23. anonymous

awesome, thanks a lot

24. anonymous

Welcome =D