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Category: Differentiation

dy-dx-y-sec-x-tan-x-

Question Number 83028 by jagoll last updated on 27/Feb/20 $$\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\mathrm{y}\:\mathrm{sec}\:\mathrm{x}\:=\:\mathrm{tan}\:\mathrm{x} \\ $$ Commented by john santu last updated on 27/Feb/20 $$\mathrm{IF}\:\Rightarrow\:\mathrm{e}^{\int\:\mathrm{sec}\:\mathrm{x}\:\mathrm{dx}} \:=\:\mathrm{e}\:^{\mathrm{ln}\:\left(\mathrm{sec}\:\mathrm{x}\:+\:\mathrm{tan}\:\mathrm{x}\:\right)\:} \\ $$$$\mathrm{IF}\:=\:\mathrm{sec}\:\mathrm{x}\:+\:\mathrm{tan}\:\mathrm{x}\: \\…

Find-the-area-between-the-curves-y-log-x-and-y-log-x-2-

Question Number 82937 by niroj last updated on 26/Feb/20 $$\:\: \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{between}\:\mathrm{the}\:\mathrm{curves} \\ $$$$\:\mathrm{y}=\:\mathrm{log}\:\mathrm{x}\:\:\mathrm{and}\:\mathrm{y}=\:\left(\mathrm{log}\:\mathrm{x}\right)^{\mathrm{2}} . \\ $$ Commented by jagoll last updated on 26/Feb/20 $$\mathrm{area}\:=\:\int\underset{\mathrm{1}}…

x-2-y-2-3-find-dy-dx-

Question Number 148324 by Odhiambojr last updated on 27/Jul/21 $${x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{3},\:{find}\:{dy}/{dx} \\ $$ Answered by liberty last updated on 27/Jul/21 $$\mathrm{2x}−\mathrm{2yy}'=\mathrm{0} \\ $$$$\Rightarrow\mathrm{y}'=\frac{\mathrm{x}}{\mathrm{y}}=\frac{\mathrm{x}}{\pm\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{3}}}\:…

show-that-if-f-x-a-x-show-that-f-x-a-x-ln-a-by-using-lim-h-0-f-x-h-f-x-h-

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…

given-dy-dx-xy-3-Determine-the-concavity-of-all-solution-curves-for-the-given-differential-equation-in-quadrant-iv-

Question Number 82521 by jagoll last updated on 22/Feb/20 $${given}\:\frac{{dy}}{{dx}}\:=\:{xy}^{\mathrm{3}} \\ $$$${Determine}\:{the}\:{concavity}\:{of}\:{all} \\ $$$${solution}\:{curves}\:{for}\:{the}\:{given}\: \\ $$$${differential}\:{equation}\:{in}\: \\ $$$${quadrant}\:{iv}.\: \\ $$ Commented by jagoll last updated…