Leibniz Notation: Finding dy/dx for y=∫e^-t dx

[thercias]

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.

 

[arildno]

e^-(ln(x))=1/x, not x as you've written. Similarly for ln(x+1)

 

[arildno]

As to your second quastion:

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