Question Number 123410 by bemath last updated on 25/Nov/20 $$\:{Suppose}\:{that}\:{f}\:{is}\:{differentiable} \\ $$$${with}\:{derivative}\:{f}\:'\left({x}\right)=\:\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{−\mathrm{1}/\mathrm{2}} . \\ $$$${Show}\:{that}\:{g}\:=\:{f}^{−\mathrm{1}} \:{satisfies}\: \\ $$$${g}''\left({x}\right)=\:\frac{\mathrm{3}}{\mathrm{2}}{g}\left({x}\right)^{\mathrm{2}} \\ $$ Answered by mnjuly1970 last…
Question Number 123407 by bemath last updated on 25/Nov/20 $${Find}\:{the}\:{all}\:{asymtotes}\:{of}\:{the} \\ $$$${curve}\:{y}\:=\:\frac{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}}{{x}−\mathrm{2}} \\ $$ Commented by EVIMENEBASSEY last updated on 25/Nov/20 $$ \\ $$$$…
Question Number 123396 by bemath last updated on 25/Nov/20 $$\:{Find}\:{the}\:{greatest}\:{and}\:{the}\:{least}\:{values} \\ $$$${of}\:{the}\:{function}\:{on}\:{indicates} \\ $$$${interval}\:\left(−\infty,\infty\right)\: \\ $$$$\left({i}\right)\:{y}\:=\:\mathrm{sin}\:{x}\:\mathrm{sin}\:\mathrm{2}{x}\:. \\ $$ Answered by TANMAY PANACEA last updated on…
Question Number 57820 by maxmathsup by imad last updated on 12/Apr/19 $${solve}\:\sqrt{{x}+\mathrm{1}}{y}^{'} −\sqrt{{x}−\mathrm{2}}{y}\:={x}^{\mathrm{2}} \:{e}^{−\mathrm{2}{x}} \:\:\:{with}\:{y}\left(\mathrm{3}\right)\:=\mathrm{1} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 57754 by malwaan last updated on 11/Apr/19 $$\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{ln}}\left(\boldsymbol{{x}}\right) \\ $$$$\left(\boldsymbol{{f}}\circ\boldsymbol{{f}}\right)'=? \\ $$ Commented by maxmathsup by imad last updated on 11/Apr/19 $${we}\:{have}\:{f}^{'} \left({x}\right)\:=\frac{\mathrm{1}}{{x}}\:\Rightarrow\:\left({fof}\right)^{'}…
Question Number 123282 by zarminaawan last updated on 24/Nov/20 $${y}−{x}\frac{{dy}}{{dx}}={a}\left({y}×{y}+\frac{{dy}}{{dx}}\right) \\ $$ Answered by Dwaipayan Shikari last updated on 24/Nov/20 $${y}−{x}\frac{{dy}}{{dx}}={ay}^{\mathrm{2}} +{a}\frac{{dy}}{{dx}} \\ $$$$\frac{{dy}}{{dx}}\left({x}+{a}\right)={y}\left(\mathrm{1}−{ay}\right) \\…
Question Number 123280 by zarminaawan last updated on 24/Nov/20 $$\frac{{dy}}{{dx}}+\left(\mathrm{sec}\:{x}\right){y}=\mathrm{tan}\:{x} \\ $$ Answered by Dwaipayan Shikari last updated on 24/Nov/20 $${I}.{F}={e}^{\int{secx}} ={secx}+{tanx} \\ $$$${y}\left({secx}+{tanx}\right)=\int{tanx}\left({secx}+{tanx}\right){dx} \\…
Question Number 188806 by horsebrand11 last updated on 07/Mar/23 $${Find}\:{minimum}\:{value}\:{of}\: \\ $$$$\:\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{xy}+\mathrm{4}{y}+\mathrm{5}{y}^{\mathrm{2}} −{x}\: \\ $$$$\:{for}\:{x}\:{and}\:{y}\:{real}\:{numbers} \\ $$ Answered by mr W last updated on…
Question Number 123243 by benjo_mathlover last updated on 24/Nov/20 $$\:{What}\:{is}\:{the}\:{shortest}\:{distance} \\ $$$${between}\:{two}\:{parabolas}\: \\ $$$${y}^{\mathrm{2}} \:=\:{x}−\mathrm{2}\:{and}\:{x}^{\mathrm{2}} \:=\:{y}−\mathrm{2}\:. \\ $$ Commented by liberty last updated on 24/Nov/20…
Question Number 123124 by aupo14 last updated on 23/Nov/20 Commented by Dwaipayan Shikari last updated on 23/Nov/20 $${x}!=\Gamma\left({x}+\mathrm{1}\right) \\ $$$${log}\left({x}!\right)={log}\left(\Gamma\left({x}+\mathrm{1}\right)\right) \\ $$$$\frac{\frac{{dx}!}{{dx}}}{{x}!}=\frac{\Gamma'\left({x}+\mathrm{1}\right)}{\Gamma\left({x}+\mathrm{1}\right)} \\ $$$$\Rightarrow\frac{{d}}{{dx}}\left({x}!\right)={x}!.\psi\left({x}+\mathrm{1}\right) \\…