## DLS 2 years ago Please find the derivative c:

1. DLS

$y=(3x^2+6x+5)^{(7/2)}$

2. cwrw238

use the chain rule ley u = 3x^2 + 6x + 5 , then y = u^(7/2) find du/dx and dy/du then dy/dx = dy/du * du/dx

3. DLS

I did the same.

4. cwrw238

ok - and what did you get?

5. cwrw238

7/2(3x^2 + 6x + 5)^(5/2) * (6x +6)

6. DLS

Im little confused.. Will it be like this? $y=\frac{(3x^{2}+6x+5)^{7/2}}{d(6x+5)} \times \frac{d(6x+5)}{d5}$ something like this? perhaps confused..

7. cwrw238

y = u^(7/2) dy/du = (7/2) u^(7/2 - 1) = (7/2) u^(5/2) substituting back for u dy/du = (7/2) ( 3x^2 + 6x + 5)^(5/2) du/dx = 6x + 6 now multiply the two results together gives (7/2)(6x+6)(3x^2 + 6x + 5)^(5/2)

8. cwrw238

with practice you won't need to do the substitution u

9. DLS

how did u get 6x+6

10. cwrw238

6x + 6 is the derivative of 3x^2 + 6x + 5 the du/dx in the above post

11. DLS

thanks!

12. cwrw238

you use chain rule when you have a 'function of a function' like this one 3x^2 +6x + 5 is the 'inside' function of (3x^2 +6x + 5)^7/2

13. cwrw238

yw

14. DLS

i have some more questions im confused with!

15. cwrw238

i'm sorry but i must go now

16. DLS

okay..

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