Question

calculus help. find the derivative of the function. g(x)=(x+5/x^2+6)^6

Answer 1

which way

Answer 2

?

Answer 3

\[(\frac{x+5}{x^2+6})^6\]

Answer 4

?

Answer 5

yeah

Answer 6

use the chain rule

Answer 7

okay the problem is that I did it i mean solves it using the chain rule and quotient but my teacher gave me

6(6-10x-x^2)(5+x)^5/(6+x^2)^7 as the answer....:[

Answer 8

alright so first you do the derivative of the outside which is

\[u^6\]

so you get

\[6u^5\]

Answer 9

then the derivative of the inside is the quotient or product rule

Answer 10

which one would you like to do?

Answer 11

either one is fine

Answer 12

alright so you have

\[\frac{h(x)g'(x)-g(x)h'(x)}{(h'(x6)^2)}\]

Answer 13

without the prime at the bottom

Answer 14

yeah

Answer 15

so h(x)=
\[x^2+6\]

and g(x)=
\[x+5\]

\[h(x)g'(x)=g(x)h'(x)= (x^2+6)(1)-(x+5)(2x)\]

Answer 16

yup :]

Answer 17

so now if you multiply everything out you're left with the top like this

\[x^2+6-2x^2-10x\]

Answer 18

yes :]

Answer 19

combine like terms you get
\[

\[-x^2-10x+6\]

Answer 20

yup

Answer 21

so now the inside is

\[\frac{-x^2-10x+6}{(x^2+6)^2}\]

Answer 22

okay got it

Answer 23

i guess my question is what did u do w. the ^6. like after u got the derivative of the inside did u just use the chain rule for it?

Answer 24

yes

Answer 25

cause now all together you have

\[(\frac{x+5}{x^2+6})^5*\frac{-x^2-10x+6}{(x^2+6)^2}\]

Answer 26

then you can take the expnent 5 and distribute it to both the numerator and denominator

Answer 27

technically if you didn't want to do the chain urle you can start by doing this

\[\frac{(x+5)^6}{(x^2+6)^6}\]

Answer 28

and then use the quotient

Answer 29

but then you'd have to do two chain rules for the quotient

Answer 30

wouldn't u only multiply by g(x) if we were doing implicit differentiation?

Answer 31

?

Answer 32

Where are you doing "implicit" differentiation?

Answer 33

never mind :l i am mistaken