Question

If f and g are differentiable functions for all real values of x such that f(1) = 4, g(1) = 3, f '(3) = −5, f '(1) = −4, g '(1) = −3, g '(3) = 2, then find h '(1) if h(x) = the quotient of f of x and g of x..
a.17
b. 11
c. 0
d. −11

Answer 1

Can you please help? @imqwerty @tkhunny @wqfqlwekfwl @123AB456C

Answer 2

I just posted a link in the math chatroom so hopefully someone will help have a great day bye! :)

Answer 3

Thank you and you have a wonderful day to! @jchick

Answer 4

Can you please help me @IrishBoy123

Answer 5

hi

Answer 6

can you please help me @DanJS

Answer 7

they define h(x) as

\[\large h(x) = \frac{ f(x) }{ g(x) }\]

take the derivative of both sides of that

Answer 8

they want h '(1)

Answer 9

I don't know how to do that because the are two f'(x) and two g'(x)

Answer 10

have to use the quotient rule , take derivative of both sides of the h(x) function with respect to x

Answer 11

How do I do that?

Answer 12

Can you write it out so I can see the steps?

Answer 13

check this
\[\large h '(x) = \frac{ g(x) * f '(x) - f(x)*g'(x)}{ [g(x)]^2 }\]

Answer 14

Okay but there is two f'(x) and two g'(x). So which ones do I use?

Answer 15

they gave you both function values and both derivative values at x=1, just put those values in to get the h'(1) value

Answer 16

yeah they want you to find h'(1) , x=1

Answer 17

so replace 1 for x in the entire problem?

Answer 18

use x=1 in h'(x) ....
\[\large h '(1) = \frac{ g(1) * f '(1) - f(1)*g'(1)}{ [g(1)]^2 }\]

Answer 19

all those values are given , fill them in

Answer 20

okay that is exactly what I got

Answer 21

so then replace g and f with the numbers given in the problem?

Answer 22

yes, all those are given

Answer 23

g(1)
f(1)
g ' (1)
f ' (1)

Answer 24

you understand it all now or no

Answer 25

yes I am trying to work it out. one second.

Answer 26

is this correct?