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Category: Differentiation

if-y-u-n-show-that-d-n-y-dx-n-n-

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-16788

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}}…

find-the-solution-x-sin-y-x-dy-y-sin-y-x-x-dx-

Question Number 82245 by jagoll last updated on 19/Feb/20 $${find}\:{the}\:{solution}\: \\ $$$${x}\:\mathrm{sin}\:\left(\frac{{y}}{{x}}\right)\:{dy}\:=\:\left[{y}\:\mathrm{sin}\:\left(\frac{{y}}{{x}}\right)\:−{x}\right]\:{dx} \\ $$ Commented by john santu last updated on 19/Feb/20 $${let}\:{v}\:=\:\frac{{y}}{{x}}\:\Rightarrow\:{y}\:=\:{vx} \\ $$$$\frac{{dy}}{{dx}}\:=\:{v}\:+\:\frac{{dv}}{{dx}}\:\Rightarrow\:{dy}\:={v}\:{dx}+\:{dv}\:…

Find-a-point-on-the-curve-y-x-2-2x-3-at-which-the-tangent-is-parallel-to-the-x-axis-

Question Number 147753 by Odhiambojr last updated on 23/Jul/21 $${Find}\:{a}\:{point}\:{on}\:{the}\:{curve} \\ $$$$\:{y}={x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{3}\:{at}\:{which}\:{the}\:{tangent}\:{is} \\ $$$$\:{parallel}\:{to}\:{the}\:{x}-{axis} \\ $$ Answered by Olaf_Thorendsen last updated on 23/Jul/21 $$\frac{{dy}}{{dx}}\:=\:\mathrm{2}{x}−\mathrm{2}\:=\:\mathrm{2}\left({x}−\mathrm{1}\right)…