Question

Please find the derivative c:

Answer 1

\[y=(3x^2+6x+5)^{(7/2)} \]

Answer 2

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

Answer 3

I did the same.

Answer 4

ok - and what did you get?

Answer 5

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

Answer 6

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..

Answer 7

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)

Answer 8

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

Answer 9

how did u get 6x+6

Answer 10

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

Answer 11

thanks!

Answer 12

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

Answer 13

yw

Answer 14

i have some more questions im confused with!

Answer 15

i'm sorry but i must go now

Answer 16

okay..