Question Number 26126 by NECx last updated on 20/Dec/17 $${using}\:\mathrm{1}{st}\:{principle}\:{find}\:{the} \\ $$$${derivative}\:{of} \\ $$$$\:\:\:\:\:\:\:\:{y}={x}^{{x}} \\ $$ Commented by abdo imad last updated on 20/Dec/17 $${answer}\:{to}\:{question}\:\:{ew}\:{have}\:{y}=\:{e}^{{xlnx}}…
Question Number 157169 by cortano last updated on 20/Oct/21 Answered by mr W last updated on 20/Oct/21 $${x}={r}\:\mathrm{cos}\:\theta \\ $$$${y}={r}\:\mathrm{sin}\:\theta \\ $$$${r}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \:\theta+\mathrm{2}{r}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}}…
Question Number 91635 by john santu last updated on 02/May/20 $${given}\:{f}\left({x}\right)=\mathrm{log}_{\mathrm{10}} \left({x}\right)\:{and}\:\mathrm{log}_{\mathrm{10}} \left(\mathrm{102}\right)\approx\mathrm{2}.\mathrm{0086} \\ $$$$,\:{which}\:{is}\:{closest}\:{to}\:{f}\:'\left(\mathrm{100}\right)? \\ $$$${A}.\:\mathrm{0}.\mathrm{0043}\:\:\:\:\:\:{B}.\mathrm{0}.\mathrm{0086} \\ $$$${C}.\:\mathrm{0}.\mathrm{01}\:\:\:\:\:\:\:\:\:\:{E}.\:\mathrm{1}.\mathrm{0043} \\ $$ Commented by mr W…
Question Number 26073 by gopikrishnan005@gmail.com last updated on 19/Dec/17 $$ \\ $$$${solve}\:{the}\:{differential}\:{equation}\left({D}^{\mathrm{2}} +\mathrm{2}{D}+\mathrm{1}\right){y}={x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1} \\ $$ Commented by gopikrishnan005@gmail.com last updated on 20/Dec/17 $${pls}\:{explain} \\…
Question Number 157116 by cortano last updated on 20/Oct/21 $$\:{max}\:\wedge\:{min}\:{of}\:{f}\left({x}\right)\:=\sqrt{{x}}\:+\mathrm{4}\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{2}}} \\ $$ Commented by cortano last updated on 20/Oct/21 $${without}\:{derivative} \\ $$ Commented by mr…
Question Number 91460 by M±th+et+s last updated on 30/Apr/20 $${one}\:{of}\:{the}\:{conditions}\:{of}\:{the}\:{inflection} \\ $$$${point}\:{is}\:{inflection}\:{tangent}. \\ $$$${what}\:{is}\:{inflection}\:{tangent}? \\ $$ Answered by MJS last updated on 01/May/20 $$\mathrm{it}'\mathrm{s}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{in}\:\mathrm{the}\:\mathrm{inflection}\:\mathrm{point}\:\mathrm{which} \\…
Question Number 25845 by NECx last updated on 15/Dec/17 $${using}\:{the}\:\mathrm{1}{st}\:{principle}\:{find}\:{the} \\ $$$${derivative}\:{of}\: \\ $$$$\:\:\:\:\:{y}=\left({ax}+{b}\right)^{{n}} \\ $$ Answered by ajfour last updated on 15/Dec/17 $$\frac{{dy}}{{dx}}=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left({ax}+{ah}+{b}\right)^{{n}}…
Question Number 156864 by mnjuly1970 last updated on 16/Oct/21 $$ \\ $$$$\:\:\:\:\phi\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{ln}\:\left(\mathrm{1}−{x}^{\:\mathrm{2}} \right)}{\mathrm{1}+\:{x}^{\:\mathrm{2}} }\:{dx}\:= \\ $$$$\:\:{proof}\:: \\ $$$$\:\:\:\:\phi\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{ln}\left(\mathrm{1}−{x}\:\right)}{\mathrm{1}+{x}^{\:\mathrm{2}} }{dx}\:+\:\frac{\pi}{\mathrm{8}}{ln}\left(\mathrm{2}\right) \\ $$$$\:\:\:\:….\:\mathrm{I}=\:\int_{\mathrm{0}}…
Question Number 91329 by niroj last updated on 29/Apr/20 $$\:\mathrm{S}\boldsymbol{\mathrm{olve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:−\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}+\boldsymbol{\mathrm{xy}}\:=\:\boldsymbol{\mathrm{x}} \\ $$ Commented by MWSuSon last updated on 30/Apr/20 $${do}\:{you}\:{need}\:{a}\:{specific}\:{method}?…
Question Number 156824 by Tawa11 last updated on 15/Oct/21 $$\mathrm{If}\:\:\:\:\:\:\mathrm{x}\:\:\:−\:\:\:\mathrm{z}\:\:\:\:=\:\:\:\:\mathrm{tan}^{−\:\mathrm{1}} \left(\mathrm{yz}\right)\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\mathrm{z}\:\:\:=\:\:\:\mathrm{z}\left(\mathrm{x},\:\:\mathrm{y}\right),\:\:\:\:\:\:\mathrm{find}\:\:\:\:\frac{\delta\mathrm{z}}{\delta\mathrm{x}}\:,\:\:\:\frac{\delta\mathrm{z}}{\delta\mathrm{y}} \\ $$ Answered by mr W last updated on 16/Oct/21 $$\mathrm{1}−\frac{\partial{z}}{\partial{x}}=\frac{{y}}{\mathrm{1}+{y}^{\mathrm{2}} {z}^{\mathrm{2}} }×\frac{\partial{z}}{\partial{x}} \\…