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  1. H

    Integrating derivatives of various orders

    Do you actually get back the integrand if you differentiate your right hand side with respect to y? (Besides that, I think your problem is easiest to answer using the Leibniz integral rule.)
  2. H

    Proving d/dx lnx = 1/x

    Why? When you make a substitution or a change of variables, you have to check how the new variable (i.e. u) depends on the original one (i.e. h). Otherwise, you'd get ridiculous results like the following (let y=2x) 2=\lim_{y\rightarrow 2} y = \lim_{x\rightarrow 2} 2x=4 EDIT: My point is that...
  3. H

    Proving d/dx lnx = 1/x

    If you let u→∞, you'll get e (which can be called Euler's number, Euler's constant usually means another number γ). Clearly, h→0 implies u→∞.