Question

Suppose that f(−4)=−8, g(−4)=5, f′(−4)=5, and g′(−4)=8. Find h′(−4) for the following.
1.) if h(x)=5f(x)−4g(x) find h'(4)
2.) if h(x)=f(x)g(x) find h'(4)
3.) if h(x)=f(x)/g(x) find h'(4)
4.) if h(x)=g(x)/(1+f(x)) find h'(4)

Answer 1

@AllTehMaffs

Answer 2

So for the first one, what does the derivative of

\[h _{(x)} = 5f_{(x)} - 4 g_{(x)}\]

look like?

Answer 3

would i just change f(x) and g(x) to f'(x) and g'(x)

Answer 4

yup! so then you know values for both f'(x) and g'(x), so just sub those values in

Answer 5

so the derivative would just be h'(x)=5f'(x)-4g'(x) and then i would plug in 5 for f'(x) and 8 for g'(x)

Answer 6

I don't get why it says to find h'(-4) for all of them up top but then find h'(4) in the question :/

I think that's what you would do - I thought it was just asking for h'(-4). You technically have no idea about what f(4) and g(4) are, but I'm guessing that's what they're wanting.

Answer 7

i mistyped its h'(-4)

Answer 8

phew! Good. then yeah, you got it.

Answer 9

i got h'(-4)=-7 for the first one

Answer 10

looks good to me

Answer 11

ok and i do that for all of them?

Answer 12

yeah. It's seeing if you know when/how to use the chain rule and such.

Answer 13

what would the second one be, then?

Answer 14

-89. i used the product rule

Answer 15

i will use the quotient rule for the last two

Answer 16

okay, yeah. Just makin' sure you didn't just switch the f and g to f' and g' :)

Answer 17

If you want to make your life easier, you can use the product rule for all of them and say

h(x) = f(x) (g(x))^-1

Answer 18

I could never remember the quotient rule :P But whatever makes sense to you is what you should use :)

Answer 19

for the last one. the derivative of 1+f(x)=f'(x)?

Answer 20

yah

Answer 21

ok

Answer 22

calculus high five

Answer 23

ummm sure

Answer 24

????

Answer 25

haha, thanks for humoring me

Answer 26

:)

Answer 27

ok i tried them i got the last three wrong

Answer 28

@AllTehMaffs

Answer 29

i got -7, -89, -89/25, 89/49

Answer 30

I got zero for the second one, actually

Answer 31

how

Answer 32

by being dumb, I'm wrong. one sec

Answer 33

for the second one you added the two parts you got. You should have subtracted 64 from 25 -- -39

Answer 34

oh ok. what about the last two

Answer 35

I got positive 89/25 for the third one

Answer 36

ok and for the last

Answer 37

still tryin it. Have another go and see if you set it right :)

Answer 38

what did you end up with?

Answer 39

89/49

Answer 40

The whole formula. I got

\[h'_{(x)} = \frac{g'_{(x)}}{(1+f_{(x)})} - \frac{g_{(x)}f'_{(x)}}{(1+f_{(x)})^{2}}\]

Answer 41

-8/7 - 25/81

Answer 42

so it would be -81/49. yup its right thanks

Answer 43

cool :)

Answer 44

addition derp on my part -8/7 - 25/49