Question

Use the table below to evaluate
d/dx {f{g(2x)}} at x = 1.

x 1 2 3 4
f(x) 6 1 8 2
f ′(x) 6 1 8 2
g(x) 1 4 4 3
g ′(x) 9 5 5 –4

Answer 1

do you know chain rule?

Answer 2

\[\frac{d}{dx}(f(g(u)))=\frac{du}{dx} \cdot g'(u) \cdot f'(g(u))\]

Answer 3

ahhhh ok

Answer 4

I guess you don't need any help?

Answer 5

you can show me what you have after applying chain rule

Answer 6

i mean i dont know how to do it

Answer 7

well i told you what chain rule is...
the only difference between your expression and my expression is that my u is your 2x

Answer 8

replace u with 2x

Answer 9

and let me know what you have after that

Answer 10

1

Answer 11

\[\frac{d}{dx}(f(g(u)))=\frac{du}{dx} \cdot g'(u) \cdot f'(g(u)) \]
did you replace u with 2x?

Answer 12

\[\frac{d(2x)}{dx} g'(2x) f'(g(2x))\]
find the derivative of 2x there at the beginning factor
then replace all the x's with 1's

Answer 13

then use your chart to evaluate