Question

Find h′(2) given that f(2) = −1, f′(2) = 4, g(2) = 1, and g′(2) = −5.

solve each one
c. h(x) = f(x)/g(x).
d. h(x) = ln f(x).

Answer 1

use the quotient rule for (c) and the chain rule for (d)

Answer 2

is the anserw to c 19

Answer 3

how did you get this answer?

Answer 4

this site might help you understand these rules better: http://www.1728.org/chainrul.htm

Answer 5

or would the anserw be 24 for c

Answer 6

it is best for you to actually show your work here rather than just giving out any final answers.
that way I can help spot where you may have made a mistake.

Answer 7

\[h'(2)=f'(2)*g(2)-f(2)*g'(2)/g(2)^2\]

Answer 8

that looks correct - so what was your next step?

Answer 9

\[h'(2)=(4)(1)-(4)(-5)/(1)^2\]
\[=4+20/1 \]
so 4 +20 =24 and 24/1 =24

Answer 10

the second (4) is not correct - it should be the value of f(2) NOT f'(2)

Answer 11

ok so it should be 4-5/1 which will give you -1 Right?

Answer 12

that is correct

Answer 13

thsnks

Answer 14

thanks lol

Answer 15

yw :)
hopefully you know how to use the chain rule for the second part?

Answer 16

well ln is 1/x and f(x) is 2 so would I do 1/2 since h'(2) and then times that by f'(x) which is 4 . not sure if its right.

Answer 17

take a look at the web site I linked to above, it also explains the chain rule further down the page. If you still don't understand it after reading that then let me know and I'll try to help.

Answer 18

I think the ln is whats confusing me for that problem

Answer 19

ok, let me do this one for you to illustrate how it works. we are given this:\[h(x)=\ln(f(x))\]lets substitute:\[y=f(x)\]so that:\[y'=f'(x)\]we then get:\[h(x)=\ln(y)\]therefore:\[\frac{dh}{dx}=\frac{dh}{dy}\times\frac{dy}{dx}=\frac{1}{y}\times f'(x)=\frac{f'(x)}{f(x)}\]

Answer 20

I hope that makes sense?

Answer 21

so I would take f'(x) and divided by f(x) ?

Answer 22

yes, h'(x) = dh/dx = f'(x)/f(x)

Answer 23

so the anserw would be -1 ?

Answer 24

please show your working...

Answer 25

\[f'(2)=4/f(2)=-1\]
so 4/-1 = -4 my bad

Answer 26

correct :)

Answer 27

Thanks !

Answer 28

yw :)