Question Number 184720 by mustafazaheen last updated on 10/Jan/23 $$ \\ $$$${y}=\left(\sqrt{\mathrm{3}{xy}^{\mathrm{2}} }\right)\left(\sqrt[{\mathrm{5}}]{{x}^{\mathrm{5}} {y}^{\mathrm{2}} }\right) \\ $$$${y}'=?\:\:\:\:\:\:{y}^{''} =? \\ $$ Answered by Frix last updated…
Question Number 118969 by benjo_mathlover last updated on 21/Oct/20 $$\:{Given}\:{f}\left({x}\right)\:=\:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}} \\ $$$${find}\:{the}\:{value}\:{of}\: \\ $$$$\:{f}\:''\left({x}\right)\:+\:{f}\:'\left({x}\right)\:+\:\mathrm{1}\:. \\ $$ Answered by TANMAY PANACEA last updated on 21/Oct/20 $${f}\left({x}\right)=\frac{{tanx}+\mathrm{1}}{{tanx}−\mathrm{1}}=−{tan}\left(\frac{\pi}{\mathrm{4}}+{x}\right)…
Question Number 53426 by Necxx last updated on 21/Jan/19 $${The}\:{general}\:{solution}\:{of}\:{the}\:{equation} \\ $$$$\frac{{dy}}{{dx}}+{ylnx}={x}^{−{x}} \\ $$$$\left.{a}\left.\right){x}^{{x}} \left(\mathrm{1}−{ce}^{{x}} \right)\:\:{b}\right)−{x}^{−{x}} \left(\mathrm{1}+{ce}^{\mathrm{2}{x}} \right) \\ $$$$\left.{c}\right)−{x}^{−{x}} \left(\mathrm{1}−{ce}^{{x}} \right) \\ $$ Commented…
Question Number 118887 by rexfordattacudjoe last updated on 20/Oct/20 Answered by benjo_mathlover last updated on 20/Oct/20 $$\:{f}\:'\left({x}\right)\:=\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{x}+{h}}\:−\sqrt{{x}}}{{h}} \\ $$$$\:=\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}+{h}−{x}}{{h}}\:×\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\:\sqrt{{x}+{h}}\:+\:\sqrt{{x}}\:} \\ $$$$=\:\mathrm{1}×\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}\:=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}} \\…
Question Number 118701 by bemath last updated on 19/Oct/20 $${What}\:{is}\:{maximum}\:{value} \\ $$$$\:{x}^{\mathrm{3}} {y}^{\mathrm{3}} \:+\mathrm{3}{xy}\:{when}\:{x}+{y}\:=\:\mathrm{8}? \\ $$ Commented by PRITHWISH SEN 2 last updated on 19/Oct/20…
Question Number 118665 by rexfordattacudjoe last updated on 19/Oct/20 Answered by bemath last updated on 19/Oct/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 184175 by mnjuly1970 last updated on 03/Jan/23 Answered by SEKRET last updated on 03/Jan/23 $$ \\ $$ Commented by SEKRET last updated on…
Question Number 118612 by rexfordattacudjoe last updated on 18/Oct/20 Answered by 1549442205PVT last updated on 18/Oct/20 $$\mathrm{y}=\mathrm{0}.\mathrm{4x}^{\mathrm{2}} −\mathrm{36x}+\mathrm{1000}= \\ $$$$\frac{\mathrm{4}}{\mathrm{10}}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{90x}+\mathrm{2500}\right)=\frac{\mathrm{2}}{\mathrm{5}}\left[\left(\mathrm{x}−\mathrm{45}\right)^{\mathrm{2}} +\mathrm{475}\right] \\ $$$$\geqslant\frac{\mathrm{2}.\mathrm{475}}{\mathrm{5}}=\mathrm{190} \\…
Question Number 118570 by rexfordattacudjoe last updated on 18/Oct/20 $${Find}\:{the}\:{dimensions}\:{of}\:{the} \\ $$$${largest}\:{rectangular}\:{garden}\:{that} \\ $$$${can}\:{be}\:{enclosed}\:{by}\:\mathrm{80}{m}\:{of} \\ $$$${fencing} \\ $$ Answered by TANMAY PANACEA last updated on…
Question Number 184040 by pete last updated on 02/Jan/23 $$\mathrm{Use}\:\mathrm{implicit}\:\mathrm{differentiation}\:\mathrm{to}\:\mathrm{find}\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} } \\ $$$$\mathrm{for}\:\mathrm{sin}{y}\:=\:{x} \\ $$ Answered by cortano2 last updated on 02/Jan/23 $${y}'\mathrm{cos}\:{y}=\mathrm{1} \\…