Need some help differentiating

  • #1
198
0
[SOLVED] need some help differentiating

Uh my bad, forgot how to differentiate ln's


Homework Statement


[tex]\frac{V_0}{xln(\frac{b}{x})} [/tex]
Find dE/dx

I can almost get the answer, but I had to use matlab to find the actual answer, so I am kind of feeling stupid now.

My problem is when I try to differentiate the ln

Homework Equations





The Attempt at a Solution



[tex]d/dx(\frac{V_0}{xln(\frac{b}{x})}) = \frac{-V_0}{x^2 ln(b/x)} + \frac{V_0 * b/x^2}{x ln(b/x)^2} =[/tex]

[tex]\frac{-V_0}{x^2 ln(b/x)} + \frac{V_0 * b}{x^3 ln(b/x)^2}[/tex]

The second term should only have x^2 in it (and no b), does anyone see where I went wrong?
 
Last edited:

Answers and Replies

  • #2
1,631
4
[tex]log_a(x)=y=>a^{y}=x[/tex] let's differentiate this implicitly, we get:

[tex]\frac{d}{dx}(a^{y}=x)=>\frac{dy}{dx}a^{y}lna=1=>\frac{dy}{dx}=\frac{1}{a^{y}lna}=>\frac{dy}{dx}=\frac{1}{xlna}[/tex]

When a=e, we get:[tex]\frac{dy}{dx}=\frac{1}{x}[/tex]. So it is just a special case of a general case.
 

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