Question Number 129026 by oustmuchiya@gmail.com last updated on 12/Jan/21 $${differentiate}\:{y}=\frac{\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}\right)^{\mathrm{2}} \sqrt{\mathrm{6}{x}+\mathrm{2}}}{{x}^{\mathrm{3}} +\mathrm{1}} \\ $$ Answered by MJS_new last updated on 12/Jan/21 $${y}=\frac{{uv}}{{w}} \\ $$$${y}'=\frac{\left({uv}\right)'{w}−{w}'{uv}}{{w}^{\mathrm{2}}…
Question Number 129028 by oustmuchiya@gmail.com last updated on 12/Jan/21 $${Find}\:{gradient}\:{of}\:{the}\:{curve}\:{y}=\frac{\mathrm{1}}{{x}−\mathrm{1}} \\ $$ Commented by liberty last updated on 12/Jan/21 $$\mathrm{m}\:=\:−\frac{\mathrm{1}}{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Terms of…
Question Number 63473 by Rio Michael last updated on 04/Jul/19 $${question} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{sin}\left({x}+{A}\right)−{sin}\left({A}−{x}\right)}{\mathrm{2}{x}} \\ $$ Commented by mathmax by abdo last updated on 04/Jul/19…
Question Number 63378 by minh2001 last updated on 03/Jul/19 $$\underset{\mathrm{2}} {\overset{{x}} {\int}}\frac{\mathrm{1}}{{x}}{dx}=\mathrm{2}{ln}\left(\mathrm{3}\right)−{ln}\left(\mathrm{2}\right) \\ $$$${please}\:{help}\:{me}\:{to}\:{solve}\:{for}\:{x} \\ $$ Answered by MJS last updated on 03/Jul/19 $$\mathrm{the}\:\mathrm{borders}\:\mathrm{must}\:\mathrm{be}\:\mathrm{independent}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{variable} \\…
Question Number 63301 by Rio Michael last updated on 02/Jul/19 $${find}\:\frac{{dy}}{{dx}}\:{if}\:\:{x}\left({x}\:+{y}\right)\:=\:{y}^{\mathrm{2}} \\ $$ Commented by kaivan.ahmadi last updated on 02/Jul/19 $${f}\left({x},{y}\right)={x}^{\mathrm{2}} +{xy}−{y}^{\mathrm{2}} =\mathrm{0} \\ $$$$\frac{{dy}}{{dx}}=−\frac{{f}'_{{x}}…
Question Number 128751 by bemath last updated on 10/Jan/21 $$\mathrm{Find}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\mid\mathrm{x}\mid\:\sqrt{\mathrm{16}−\mathrm{y}^{\mathrm{2}} }\:+\:\mid\mathrm{y}\mid\:\sqrt{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }\:\mathrm{for}\:\mathrm{all}\:\mathrm{real}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}. \\ $$$$ \\ $$ Answered by mr W last updated on…
Question Number 63152 by Rio Michael last updated on 29/Jun/19 $${The}\:{Variables}\:{x}\:{and}\:{y}\:{satisfy}\:{the}\:{differential}\:{equation}\: \\ $$$$\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−{x}\frac{{dy}}{{dx}}\:+\:{y}\:=\:{x}^{\mathrm{2}} \:\:{use}\:{the}\:{approximations} \\ $$$$\:\:\:\left(\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\right)_{{n}} \approx\:\frac{{y}_{{n}+\mathrm{1}} −\mathrm{2}{y}_{{n}} +{y}_{{n}−\mathrm{1}} }{{h}^{\mathrm{2}\:} }\:{and}\:\:\left(\frac{{dy}}{{dx}}\right)\approx\frac{{y}_{{n}+\mathrm{1}}…
Question Number 63128 by Tawa1 last updated on 29/Jun/19 $$\mathrm{Examine}\:\mathrm{the}\:\mathrm{following}\:\mathrm{function}\:\mathrm{for}\:\mathrm{extreme}\:\mathrm{value} \\ $$$$\:\:\:\:\mathrm{f}\left(\mathrm{x},\:\mathrm{y}\right)\:\:=\:\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:−\:\mathrm{2x}^{\mathrm{3}} \:+\:\mathrm{4xy}\:−\:\mathrm{2y}^{\mathrm{2}} \\ $$ Commented by Hope last updated on 29/Jun/19 Commented…
Question Number 63015 by ajfour last updated on 27/Jun/19 $${f}\left({x},{y},{z}\right)=\:{x}\left({p}+{z}\right)+{y}\left({p}−{z}\right) \\ $$$$\:\:\:\:+\frac{\mathrm{4}{x}^{\mathrm{3}} }{{p}+{z}}+\frac{\mathrm{4}{y}^{\mathrm{3}} }{{p}−{z}}+\mathrm{4}\left({x}+{y}\right)^{\mathrm{2}} \left({y}−{x}\right) \\ $$$$\forall\:\:{p}\left({x},{y}\right)={c}+\left({x}−{y}\right)\sqrt{\mathrm{1}+\left({x}+{y}\right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right) \\ $$$${Determine}\:{x},{y},{z}\:{such}\:{that}\:{f}\:{is} \\…
Question Number 128521 by bramlexs22 last updated on 08/Jan/21 $$\mathrm{A}\:\mathrm{curve}\:\mathrm{has}\:\mathrm{equation}\:\mathrm{y}\:=\:\left(\mathrm{2}−\sqrt{\mathrm{x}}\:\right)^{\mathrm{4}} \\ $$$$\mathrm{The}\:\mathrm{normal}\:\mathrm{at}\:\mathrm{point}\:\mathrm{P}\left(\mathrm{1},\mathrm{1}\right)\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{normal}\:\mathrm{at}\:\mathrm{point}\:\mathrm{Q}\left(\mathrm{9},\mathrm{1}\right)\:\mathrm{intersect} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\mathrm{R}.\:\mathrm{What}\:\mathrm{are}\:\mathrm{coordinates} \\ $$$$\mathrm{at}\:\mathrm{point}\:\mathrm{R}? \\ $$ Answered by mr W last…