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Category: Differentiation

Question-194467

Question Number 194467 by horsebrand11 last updated on 08/Jul/23 $$\:\:\:\underline{\downdownarrows} \\ $$ Answered by mr W last updated on 08/Jul/23 $${f}\left({x}\right)=\sqrt{\mathrm{4}^{\mathrm{2}} −\left({x}−\mathrm{4}\right)^{\mathrm{2}} }−\sqrt{\mathrm{1}^{\mathrm{2}} −\left({x}−\mathrm{7}\right)^{\mathrm{2}} }…

X-

Question Number 194325 by horsebrand11 last updated on 03/Jul/23 $$\:\:\cancel{\mathcal{X}} \\ $$ Answered by AST last updated on 04/Jul/23 $$\sqrt[{\mathrm{4}_{} }]{\frac{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} }{\mathrm{3}}}\geqslant\sqrt{\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}}…

Question-194088

Question Number 194088 by cortano12 last updated on 27/Jun/23 Answered by horsebrand11 last updated on 27/Jun/23 $$\:\mathrm{y}^{\mathrm{2}} =\:\left(\mathrm{2}+\left(\mathrm{x}+\mathrm{x}^{\mathrm{2}} \right)\right)\left(\mathrm{1}−\left(\mathrm{x}+\mathrm{x}^{\mathrm{2}} \right)\right) \\ $$$$\:\mathrm{let}\:\mathrm{x}+\mathrm{x}^{\mathrm{2}} =\:\mathrm{u} \\ $$$$\:\mathrm{y}^{\mathrm{2}}…

Question-193847

Question Number 193847 by Mingma last updated on 21/Jun/23 Answered by witcher3 last updated on 21/Jun/23 $$=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)}{\mathrm{x}}\mathrm{dx}=−\mathrm{Li}_{\mathrm{2}} \left(\mathrm{1}\right)=−\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}=\Sigma\mathrm{x}^{\mathrm{k}} \\ $$$$=\int_{\mathrm{0}}…

f-x-2-0-x-2t-f-t-2-dt-then-1-2-f-x-dx-

Question Number 193768 by cortano12 last updated on 19/Jun/23 $$\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{2}+\underset{\mathrm{0}} {\overset{\:\mathrm{x}} {\int}}\left(\mathrm{2t}+\mathrm{f}\left(\mathrm{t}\right)\right)^{\mathrm{2}} \mathrm{dt}\: \\ $$$$\:\:\mathrm{then}\:\underset{−\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:= \\ $$ Answered by gatocomcirrose last updated on…

Question-193486

Question Number 193486 by Mingma last updated on 15/Jun/23 Answered by Subhi last updated on 15/Jun/23 $${x}^{{x}} .{ln}\left({x}\right)={ln}\left({y}\right) \\ $$$${ln}\left({x}^{{x}} .{ln}\left({x}\right)\right)={ln}\left({ln}\left({y}\right)\right)\Rrightarrow\:{xln}\left({x}\right)+{ln}\left({ln}\left({x}\right)\right)={ln}\left({ln}\left({y}\right)\right) \\ $$$${ln}\left({x}\right)+{x}.\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{x}.{ln}\left({x}\right)}=\frac{\mathrm{1}}{{y}.{ln}\left({y}\right)}.\frac{{dy}}{{dx}} \\ $$$$\frac{{dy}}{{dx}}={x}^{{x}}…