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# core 3 differentiation watch

1. For each of the following curves, find dy/dx and determine the exact x-coordinate of the stationary point:
y= x^2/lnx

i know that to differentiate this, i need to use the quotient rule:
dy/dx = (lnx2x - x^2*1/x)/ (lnx)^2
i made dy/dx equal to zero but i'm not sure how to solve this after that?
2. (Original post by elvss567)
For each of the following curves, find dy/dx and determine the exact x-coordinate of the stationary point:
y= x^2/lnx

i know that to differentiate this, i need to use the quotient rule:
dy/dx = (lnx2x - x^2*1/x)/ (lnx)^2
i made dy/dx equal to zero but i'm not sure how to solve this after that?
You have numerator = 0 so then just factor out the x
3. (Original post by RDKGames)
You have numerator = 0 so then just factor out the x
if i factor out x, i got:
x(ln2 - x*1/x) / (lnx)^2

the mark scheme says if i solve this, i must get x=e^1/2. how do i get this?
4. (Original post by elvss567)
if i factor out x, i got:
x(ln2 - x*1/x) / (lnx)^2

the mark scheme says if i solve this, i must get x=e^1/2. how do i get this?
Set it =0 then it’s obvious!
5. (Original post by RDKGames)
Set it =0 then it’s obvious!
I genuinely cant see it? could you elaborate please?
6. ->
So, first solution is 0, and the next solution will be when you solve
7. (Original post by elvss567)
I genuinely cant see it? could you elaborate please?

Set it =0 then clearly you have ... so either or . Former case is not possible.

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