Question

Calculate the requested derivative from the given information.
Given f(u)=u^3and g(x) =u=x+4/x-2,find (f of g)'(3).

Answer 1

knowing f(x) = x^3 and g(x) = x + 4/(x - 2), can you determine f(g(x)) ? if so, you can determine f(g(x))'

Answer 2

Ok let me see

Answer 3

So it would start off ... (x+4/x-2)^3

Answer 4

right.

is that \[x + 4/x - 2\] or \[x + \frac{ 4 }{ x - 2 }\]
?

Answer 5

The first one

Answer 6

ah ok.

Answer 7

So next would be ....... 3(x+4/x−2)

Answer 8

yes you have to determine the following derivative:
\[\frac{ d }{ dx } (x + \frac{ 4 }{ x } - 2)^3\]

Answer 9

Huh? I don't know how you got that

Answer 10

do you agree that\[f(g(x)) =( x + \frac{ 4 }{ x } - 2)^3\]
?

Answer 11

No, how did it come from x+4 to (x+4x−2)3
_____
x-2

Answer 12

you stated\[g(x) = x + \frac{ 4 }{ x } - 2\] ?

Answer 13

no, g(x) is x+4
x-2

Answer 14

\[f(g(x)) = \left( \frac{ x + 4 }{ x - 2 } \right)^3\]
?

Answer 15

yes

Answer 16

ah ok. so we just need to take the derivative of that thing. then evaluate it at x = 3

Answer 17

3 * ( (x+4/x−2)^ 1/2 ?

Answer 18

i get \[3\left( \frac{ x + 4 }{ x - 2 } \right)^2 * \frac{ (x - 2) - (x + 4) }{ (x - 2)^2 }\]

Answer 19

using chain rule, then quotient rule

Answer 20

ok, let me see, what I get

Answer 21

ok i got that

Answer 22

so how is the answer -882

Answer 23

i got the same answer

Answer 24

how?

Answer 25

let x = 3, and solve

Answer 26

\[f(g(x))' = 3\left( \frac{ x+4 }{ x - 2 } \right)^2 * \frac{ (x - 2) - (x + 4)}{ (x - 2)^2 }\]
\[f(g(3))' = 3\left( \frac{ 3+4 }{ 3 - 2 } \right)^2 * \frac{ (3 - 2) - (3 + 4) }{ (3 - 2)^2 }\]
\[ = 3*7^2 * -6 = -882\]

Answer 27

oh, I didn't square the 7 at first. but i got it now , thans