Leibniz notation

  • Thread starter thercias
  • Start date
  • #1
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Homework Statement


Using Leibniz's rule to find dy/dx for
y = integral of e^-t from interval: [ln(x) to ln(x+1)]


Homework Equations





The Attempt at a Solution


dy/dx = e^-(ln(x+1))*(1/(1+x))-e^-(ln(x))*(1/x)
= (x+1)/(1+x) - (x/x)
= 0

Im not sure what I'm doing wrong or how to properly use leibniz's rule... i checked wolfram alpha and my answer doesn't look right.

also side question, my teacher manages to simplify integral of (x^2)/(x^2+a^2)^2 to (integral 1/(x^2+a^2) - a^2*integral(1/(x^2+a^2)^2)
if you have a clue on how he reaches to that conclusion i would appreciate it.
 

Answers and Replies

  • #2
arildno
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e^-(ln(x))=1/x, not x as you've written. Similarly for ln(x+1)
 
  • #3
arildno
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As to your second quastion:

Replace your numerator with the device x^2=(x^2+a^2)-a^2
 

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