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Category: Differentiation

y-x-4ln-x-

Question Number 83131 by 09658867628 last updated on 28/Feb/20 $${y}=\boldsymbol{{x}}^{\mathrm{4ln}\:\boldsymbol{{x}}} \\ $$ Commented by mr W last updated on 28/Feb/20 $${dear}\:{sir}: \\ $$$${please}\:{stop}\:{posting}\:{the}\:{same}\:{questions} \\ $$$${more}\:{times}!\:{if}\:{it}\:{occurs}\:{by}\:{mistake},…

let-a-b-two-positive-reals-such-as-a-2-b-2-ab-Explicit-f-a-b-0-pi-2-du-a-bsin-2-u-

Question Number 83042 by ~blr237~ last updated on 27/Feb/20 $${let}\:\:{a},{b}\:{two}\:{positive}\:{reals}\:{such}\:{as}\:\:{a}^{\mathrm{2}} −{b}^{\mathrm{2}} ={ab} \\ $$$${Explicit}\:\:\:{f}\left({a},{b}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{du}}{\:\sqrt{{a}+{bsin}^{\mathrm{2}} {u}}}\: \\ $$ Commented by mathmax by abdo last…

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}}}\:…