Category: Differentiation

Question Number 82546 by M±th+et£s last updated on 22/Feb/20 $${show}\:{that}\: \\ $$$${if}\:{f}\left({x}\right)={a}^{{x}} \\ $$$$ \\ $$$${show}\:{that}\:{f}\:'\left({x}\right)={a}^{{x}} \:{ln}\left({a}\right) \\ $$$$ \\ $$$${by}\:{using}\:\underset{{h}\rightarrow\mathrm{0}} {{lim}}\frac{{f}\left({x}+{h}\right)−{f}\left({x}\right)}{{h}} \\ $$ Commented…

Question Number 16893 by chux last updated on 27/Jun/17 $$\mathrm{if}\:\mathrm{y}=\mathrm{u}^{\mathrm{n}} \:\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{d}^{\mathrm{n}} \mathrm{y}/\mathrm{dx}^{\mathrm{n}} =\mathrm{n}! \\ $$ Commented by mrW1 last updated on 28/Jun/17 $$\mathrm{if}\:\mathrm{y}=\mathrm{u}^{\mathrm{n}} \:\:\:\mathrm{then}\:\mathrm{d}^{\mathrm{n}} \mathrm{y}/\mathrm{dx}^{\mathrm{n}}…

Question Number 82350 by jagoll last updated on 20/Feb/20 $$\mathrm{2}{y}''\:+\mathrm{5}{y}'\:−\mathrm{3}{y}=\mathrm{0} \\ $$$${general}\:{and}\:{particular}\:{solution} \\ $$$${when}\:{x}\:=\mathrm{0}\:,\:{y}\:=\:\mathrm{4}\:{and}\:\frac{{dy}}{{dx}}\:=\:\mathrm{9}? \\ $$ Commented by jagoll last updated on 20/Feb/20 Terms of…

Question Number 16788 by jyoti5726 last updated on 26/Jun/17 Commented by 1234Hello last updated on 04/Jul/17 $$\mathrm{tan}^{−\mathrm{1}} \:\sqrt{\mathrm{3}}\:=\:\frac{\pi}{\mathrm{3}} \\ $$$$\mathrm{sec}^{−\mathrm{1}} \:\left(−\mathrm{2}\right)\:=\:\mathrm{cos}^{−\mathrm{1}} \:\left(\frac{−\mathrm{1}}{\mathrm{2}}\right)\:=\:\frac{\mathrm{2}\pi}{\mathrm{3}} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \:\sqrt{\mathrm{3}}\:−\:\mathrm{sec}^{−\mathrm{1}}…

Question Number 82247 by jagoll last updated on 19/Feb/20 $$\left({D}^{\mathrm{4}} +\mathrm{2}{D}^{\mathrm{2}} +\mathrm{1}\right){y}\:={x}^{\mathrm{2}} \:\mathrm{cos}\:{x}\: \\ $$ Commented by john santu last updated on 20/Feb/20 $${characteristic}\:{equation}\: \\…