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 &theta;" 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 d&theta; in BOTH denominators, and not in the sec2 &theta; 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 d&theta; in NONE of the three denominators, but appearing explicitly in the sec2 &theta; term. You can't divide one of these by d&theta; without dividing AL THREE of them by d&theta;. 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
 * $$\begin{align} u^2 & = w, \\ 2u\,du & = dw. \end{align} $$

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