User talk:Tal physdancer

I cannot fully agree with your edit that I corrected here. Part of what you did was right: the d in front of "tan θ" should have been there and was not. If

$\tan \theta ={\frac {x-4}{3}}$

then

${\frac {d}{d\theta }}\tan \theta =\sec ^{2}\theta ={\frac {dx}{3\,d\theta }},$

with dθ in BOTH denominators, and not in the sec² θ term, and that's just equality of derivatives. It is equivalent to saying

$d\tan \theta =\sec ^{2}\theta \,d\theta ={\frac {dx}{3}},$

with dθ in NONE of the three denominators, but appearing explicitly in the sec² θ term. You can't divide one of these by dθ without dividing AL THREE of them by dθ. So I left the article with just the last line above, that being typical of what one does in such substitutions, as for example when one writes

${\begin{aligned}u^{2}&=w,\\2u\,du&=dw.\end{aligned}}$

Michael Hardy (talk) 22:15, 7 May 2009 (UTC)