Product rule calculus help

1. Mar 5, 2005

footprints

y = x ln x

$$\frac{dy}{dx} = \frac{1}{x ln x} \cdot 1$$

Is that correct?

2. Mar 5, 2005

vincentchan

wrong... use product rule

$$\frac{d}{dx} (fg) = \frac{df}{dx}g+f\frac{dg}{dx}$$

3. Mar 5, 2005

footprints

And how would that look like? Which is f & which one is g?

4. Mar 5, 2005

SphericalStrife

Hmm i'm not great at this but,

y = x lnx
I was gunna say.. that whenever you take the derivative of logs.. 1/function * derivative of that function
so that'd give you
y = (1/xlnx)(1/x)
but by using the product rule...
y = 1(xlnx) + x(1/x))
Hmm, definately don't listen to me, i don't know WHats going on. Here to learn!

5. Mar 5, 2005

footprints

I was taught that way. How did you get 1/x?

6. Mar 5, 2005

SphericalStrife

hmm I think i might just be being stupid. 1/x is the known derivative of lnx.. but i guess with that other x there.. x lnx, you would need to use product rule like that guy said?

7. Mar 5, 2005

footprints

Oh I see...
How do you know it?

8. Mar 5, 2005

Yegor

Use product rule. f(x)=x and g(x)=ln(x)
Now just find derivatives
y = x'*lnx + x*ln(x)'

9. Mar 5, 2005

footprints

Yeah I got it. Thank you.