Question

PLEASE HELP!
See attached graph
If f and g are functions whose graphs are shown, let u(x)=f(g(x)), v(x)=g(f(x)) and w(x)=g(g(x)). Find each derivative. If it exists. If it does not exist explain why.
a.) u'(1)
b.)v'(1)
c.)w'(1)

Answer 1

u'(x)=f'(g(x)) * g'(x)
u'(1)=f'(g(1)) * g'(1)
Now can u tell me g(1)?

Answer 2

3

Answer 3

g(1)=3
f(1)=2
f'(1)=2
I don't know what g'(1) is

Answer 4

Thus u'(1)=f'(3)*g'(1)
To solve this remember the relation b/n derivative and slope of a line.

Answer 5

to find f'(3) use these two points (2, 4) & (6, 3), tghen find the slope b/n the two points
Can u do that?

Answer 6

So it would be 1/4

Answer 7

- 1/4

Answer 8

And can do the same thing for g'(1)?

Answer 9

So it would be it be -3?

Answer 10

correct, then u'(1).....?

Answer 11

It would be 3/4

Answer 12

That is it.

Answer 13

I think U will finish b and c by Ur self.
Isn't it?

Answer 14

I know that the next one isn't supposed to exist but I don't know why

Answer 15

Could you please help explain why?

Answer 16

It exists

Answer 17

sorry u correct it isn't exist.

Answer 18

This why

Answer 19

v'(x)=g'(f(x)) * f'(x)
v'(1)=g'(f(1))*f'(1)
v'(1)=g'(2) * 2
But g'(2) is not exist.
This is b/c at x = 2 the graph makes a sharp corner.

Answer 20

I see thank you for your help

Answer 21

well come

Answer 22

So would w'(1) be g'(3)*g(1)?

Answer 23

So would you have 3*then g'(3)*3?

Answer 24

w'(1)=g'(g(1)) * g'(1)
w'(1) = g'(3) * 3
w'(1) = (2/3) *3
w'(1) =2

Answer 25

did u get it?