Question

suppose that (g(x))^2+6x=x^2g(x)+17 and g(2) =5 find g'(2)

Answer 1

Please.. i need help for the answer.. this is due tonight and i need to get it done!

Answer 2

Have you differentiate the right side yet?
That is the side I seen you last working on.

Answer 3

yes, 3g(x)2?

Answer 4

3g(x)^2

Answer 5

wait are you trying to do left side or tight side
because well that is neither side differentiated correctly...

Answer 6

\[\frac{d}{dx}(g(x))^2=2g(x)\cdot g'(x) \ \text{ By chain rule } \\ \frac{d}{dx}6x =?\text{ I will leave this one for you } \\ \frac{d}{dx} (x^2g(x))=(x^2)'g(x)+x^2(g(x))' \text{ By product rule } \]

Answer 7

6

Answer 8

ok and finish up that last line too

Answer 9

i was trying to do the right side, isnt the left side 2(g(x))g'(x)+6?

Answer 10

yes your left hand side is right

Answer 11

ok then is the right side 2x*g(x)

Answer 12

the g(X) throws me off a little

Answer 13

did you see my last line above with the pretty latex?

Answer 14

ok so its (x^2) g(x) +x^2(g(x))

Answer 15

You need to differentiate the parts that are in ( )'

Answer 16

x^2' g(x) + x^2 (g(x))'

Answer 17

(x^2)'=2x...
(g(x))'=g'(x)

Answer 18

would 2x stay prime or no

Answer 19

oh nvm

Answer 20

i got confused for a sec

Answer 21

(x^2)''=(2x)'=2
But we had (x^2)'

Answer 22

and (x^2)'=2x

Answer 23

2x g(x) +x^2 g(x)

Answer 24

not exactly

Answer 25

Are you not familiar with product rule?

Answer 26

i did learn it but i was last week so its not clear in my head

Answer 27

it*

Answer 28

\[(uv)'=u'v+v'u \\ (x^2g(x))'=(x^2)'g(x)+g'(x)x^2 \\ (x^2g(x))'=2xg(x)+g'(x)x^2 \]

Answer 29

okay thank you, now do i plug in 2?

Answer 30

yes
replace the x's with 2

Answer 31

then solve for g'(2)

Answer 32

don't forget to replace g(2) with 5

Answer 33

ok.. to verify my answeer

Answer 34

freckles

Answer 35

\[2g(x)g'(x)+6=2xg(x)+g'(x)x^2 \\ 2g(x)g'(x)-g'(x)x^2=2xg(x)-6 \\ g'(x)[2g(x)-x^2]=2xg(x)-6 \\ g'(x)=\frac{2xg(x)-6}{2g(x)-x^2}\]

Answer 36

Replace x's with 2's

Answer 37

\[g'(2)=\frac{2(2)g(2)-6}{2g(2)-2^2}\]

Answer 38

you are give g(2) is 5
so replace g(2) with 5

Answer 39

yeah, did u get 14/6

Answer 40

yup its right