Question

Let H(x)=F(G(x)) and J(x)=F(x)/G(x). Suppose
F(2)=5, F′(2)=5
G(2)=9, G′(2)=0
G(−8)=2, G′(−8)=−6
then
H(−8)=

H′(−8)=

J(2)=

J′(2)=

Answer 1

I am thinking that product and quotient rule are both used but I am not sure

Answer 2

H(-8)=2 is wrong

Answer 3

Why is it wrong?

Answer 4

Oh
My bad, it should be 5.

Answer 5

Sorry about that.

Answer 6

its okay

Answer 7

for first one you need to apply chain rule
there is function inside the function \[\huge\rm H(x)= F(\color{ReD}{G(x)})\]
\[\rm =f'(g(x)) \cdot g'(x)\] i guess

Answer 8

plugin -8 for x to find h(-8)

Answer 9

@Nnesha which problem are you referring to?

Answer 10

to find H(-8) you need to use first function.

Answer 11

okay

Answer 12

For the method you mentioned I would have H(x)=(2*5)(-6)

Answer 13

@Nnesha

Answer 14

no that's not correct.

Answer 15

\[\huge\rm H(x)= F(\color{ReD}{G(x)})\]
\[\rm =f'(\color{blue}{g(-8)}) \cdot g'(-8)\]

G(-8)= ???

Answer 16

2

Answer 17

right so replace g(-8) by 2
\[\rm =f'(\color{blue}{2 }) \cdot g'(-8)\]
make sense now ?

Answer 18

so its 5*-6

Answer 19

yep

Answer 20

this is for H(-8) correct?

Answer 21

yes

Answer 22

the answer is 5 but the answer I would of gotten would have been -30

Answer 23

ahh i see there are two different questions
H(-8)
AND H'(-8)
the one we did is the 2nd one where we have to take derivative

Answer 24

oh okay

Answer 25

the first is simple: just pluggin n numbers

Answer 26

one*

Answer 27

I am confused on how to do the H'(-8) though

Answer 28

H'(-8) =
means take the derivative when x=-8
so you have to apply the chain rule there

Answer 29

ok ill try it

Answer 30

how do i do the chain rule for this part? i know the derivative of x=-8 is -6, but im lost after that

Answer 31

@Nnesha

Answer 32

what do you mean "derivative of x = -8" ??
first you need to replace x by -8 \[\large\rm H(-8)= F(\color{blue}{G(-8)})\]
and then take derivative

Answer 33

So when you do this you take the derivative of the outside leaving the inside the same like @Nnesha is saying so you will have F(G(x)) so take the derivative of the outside leaving the inside unchanged times the derivative of the anside and than stay with you unchanged term because that's the on,y part that has an x term for the first part of the equation

Answer 34

So what is the derivative of f and g

Answer 35

right side : there is a function inside the function so you have to do chain rule
here is an example \[\large\rm f(\color{Red}{g(x)}) = f'(\color{red}{g(x)}) \cdot \color{blue}{g'(x)}\]
take the derivative of outer function (inside function would stay the same )
and then multiply by the derivative of inner function

Answer 36

so does H'(-8)=-12?

Answer 37

how did you get that ??

Answer 38

oh wait. OMG! I am so dumb lol

Answer 39

H'(-8)=-30; I am sorry, I've had a long day :D

Answer 40

no you're not.

Answer 41

yep looks good o^_^o

Answer 42

Two college midterms in one day is exhausting

Answer 43

better than essay ;(