Category: Differentiation

Question Number 139878 by bramlexs22 last updated on 02/May/21 $$\mathrm{I}\left(\alpha \right)=\underset{\alpha }{\stackrel{{\alpha }^2}{\int }}\frac{\sin \alpha \mathrm{x}}{\mathrm{x}}\mathrm{dx}$$$$\frac{\mathrm{dI}\left(\alpha \right)}{\mathrm{d}\alpha }=?$$ Answered by EDWIN88 last updated on 02/May/21 $$\:\:\:\:\:\frac{\mathrm{dI}}{\mathrm{d}\alpha}\:=\:\underset{\alpha}…

Question Number 74235 by aliesam last updated on 20/Nov/19 Answered by Joel578 last updated on 20/Nov/19 $$\mid x\mid =\sqrt{x^2}$$$$f\left(x\right)=\sqrt{{(x^2-3)}^2}$$$${f}\:'\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\left({x}^{\mathrm{2}} \:−\:\mathrm{3}\right)^{\mathrm{2}}…

Question Number 8488 by Basant007 last updated on 12/Oct/16 $$find{y}_{n}ify=\cos 2x$$ Commented by FilupSmith last updated on 13/Oct/16 $${y}_{{n}} =\frac{{d}^{{n}} {y}}{{dx}^{{n}} } \…

Question Number 139479 by mnjuly1970 last updated on 27/Apr/21 $$\dots .advanced\dots .★★★\dots ..calculus\dots ..$$$$:=\underset{n=1}{\sum ^{\mathrm{\infty }}}{\left(\frac{sin\left(n\right)}{n}\right)}^3=?$$$$$$ Answered by Dwaipayan Shikari last…

Question Number 139404 by mnjuly1970 last updated on 26/Apr/21 $$$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$proof::\underset{n=-\mathrm{\infty }}{\sum ^{\mathrm{\infty }}}{\left(\frac{sin\left(n\right)}{n}\right)}^2=\pi$$$$\dots \dots .nice.calculus\dots \dots$$ Answered by Dwaipayan Shikari…