Ch2-Preliminary calculus
Mathematical Methods for Physics and Engineering 1. Basic derivatives of some functions [Page 44] $$\frac{d}{dx}sec(ax)=asec(ax)tan(ax)\\ \frac{d}{dx}tan(ax)=asec^2(ax)\\ \frac{d}{dx}cosec(ax)=-acosec(ax)cot(ax)\\ \frac{d}{dx}cot(ax)=-acosec^2(ax)\\ \frac{d}{dx}sin^{-1}\frac{x}{a}=\frac{1}{\sqrt{a^2-x^2}}\\ \frac{d}{dx}cos^{-1}\frac{x}{a}=\frac{-1}{\sqrt{a^2-x^2}}\\ \frac{d}{dx}tan^{-1}\frac{x}{a}=\frac{a}{a^2+x^2}\\ Leibnitz’ theorem:(uv)^{(n)}=\sum\limits_{r=0}^{n}{}^{n}C_ru^{(r)}v^{(n-r)}$$ 2. Some properties of curves [Page 44,49,51,53-56] $\frac{df}{dx}=0,\frac{d^2f}{dx^2}>0\Rightarrow Minimum;\frac{df}{dx}=0,\frac{d^2f}{dx^2}<0\Rightarrow Maximum$ . $$\frac{df}{dx}=0,\frac{d^2f}{dx^2}=0\Rightarrow a\ stationary\ point\ of\ inflection\\(\frac{d^2f}{dx^2}…
