Question

given dy/dx[f(2x)]=f'(x) and f'(1)=1, find f'(2)

Answer 1

@Hero and @FibonacciChick666 please help

Answer 2

@thomaster

Answer 3

ok, so can you tell me what dy/dx stands for?

Answer 4

also, do you have more information?

Answer 5

No more info, and dy/dx is the change in y in respect to the change in x

Answer 6

ok hmm, this is interesting, I have a theory for the problem, but I can't guarantee it

Answer 7

integrate both sides wrt x , what do you get?

Answer 8

or WAIT easier

Answer 9

can you re-write f'(x)?

Answer 10

in general

Answer 11

I tried thinking that since they said \[\Large \frac{ dy }{ dx }\left[ f(2x) \right]=f \prime (x)\]

Answer 12

what did you get?

Answer 13

Isn't it \[\Large f \prime (2x)=f \prime (x) \]

Answer 14

or was the answer wrong?

Answer 15

yea, that's what I'm thinking

Answer 16

ok and here are hte answer choices sorry I should've included those

Answer 17

1/4

1/2

3/4

3/2

5/2

Answer 18

what? that's weird

Answer 19

exactly I'd assume that there would be 1 as an answer

Answer 20

uhm , I have to go but, let's see. we'd need dy/dx f(4)=f'(2)

Answer 21

so maybe something where you split upthe four into f(1)+f(1)+f(1) but I'm not sure

Answer 22

Hmm, ok thanks anyways

Answer 23

this doesn't make sense to me, @ganeshie8 , any ideas?

Answer 24

\[\Large\rm \frac{d}{dx}f(2x)=f'(x)\]Apply chain rule to the left side,\[\Large\rm 2f'(2x)=f'(x)\]Evaluate this at x=1,\[\Large\rm 2f'(2)=f'(1)\]Understand how to wrap it up? :)

Answer 25

That's so cool!

Answer 26

Ya it's a neat problem!
I remember seeing this one like a month ago or something like that.

Answer 27

So it'd be 1/2 since the LHS is 1 and you divide by 2 on both sides to just get f'(2)

Answer 28

Yah looks good!

Answer 29

@FibonacciChick666 yeahhh

Answer 30

oh wow I overcomplicated. Sorry, but yea, I can see that working now, as a side note though, that means that every derivative should have the same value since 2x changes to just 2, so you can't get 1 for f'(1) but anyways, go with what zepdrix said becasue it's a better lead than I had