Question

If f(x) = 2 x^{2 x}, find f'( 2 ).

Answer 1

\[If f(x) = 2 x^{2 x}, find f'( 2 )\]

Answer 2

dont u need to only plug the 2 into the x?

Answer 3

Yah after I find the derivativve wwhich I dont know how

Answer 4

No, you have to find the derivative and then plug 2 into that.

Answer 5

what's a derivative?

Answer 6

Can someone help me find the derivative

Answer 7

Okay...\[{d \over dx} 2x^{2x} \implies 2{d \over dx}x^{2x}\]Chain rule now

Answer 8

Okay so is it 2x*2x*2 ?

Answer 9

4*4*2?

Answer 10

Erm, no.

Answer 11

dang it!

Answer 12

You have to use the Chain Rule, Monique.

Answer 13

I thThere is no exponent rule?

Answer 14

ohh I pull the 2 out

Answer 15

There's no power rule for this one, but you can pull the constant coefficients out, yes.

Answer 16

this is an example of log diff.
let I= x^{2x}
take log on both sides, what u get ?

Answer 17

4x*x*2?

Answer 18

oh wait

Answer 19

darn it

Answer 20

You can use @hartnn's method too. I learnt it that way, originally!

Answer 21

I think that you are comfortable with @hartnn's method if you understand what logarithms are.

Answer 22

lny=2xlnx

Answer 23

Either use @hartnn method by solving for g(x) = ln(f(x)) and finding first g`(x), or use chain rule by writing f(x,y)=x^y and y=2x, than diferentiate.

Answer 24

Still lost

Answer 25

Let's turn out with something easy ;)\[a^b = c \implies \log_a c =b\]\[x^{2x} = l\implies \log_x l = 2x\]

Answer 26

CANNOT USE CHAIN RULE HERE
only log diff.

Answer 27

Help me!!!!

Answer 28

I = x^(2x)
log I = 2x log x .....(log here is natural log ln)
ok with 1st step ?

Answer 29

what is the l?

Answer 30

lny=2x ln x

Answer 31

I is anything... i mean u can take y also
so yes, ln y = 2x ln x
now u know if u now differentiate, how would u diff ln y ??

Answer 32

Im a little confuesed on how to differentiate this

Answer 33

ok,
\(\huge \frac{d}{dx}lny=\frac{1}{y}\quad\frac{dy}{dx}\)
ok ?

Answer 34

can i assume u can differentiate the right side using product rule ??