Question Number 11571 by Nayon last updated on 28/Mar/17 $${why}\:\:\:\frac{{d}\left[{f}\left\{{g}\left({x}\right)\right\}\right]}{{dx}}=\frac{{df}\left[\left\{{g}\left({x}\right)\right\}\right]}{{dg}\left({x}\right)}.\frac{{dg}\left({x}\right)}{{dx}}? \\ $$ Answered by mrW1 last updated on 28/Mar/17 $${y}={f}\left({u}\right) \\ $$$${u}={g}\left({x}\right) \\ $$$$\frac{{dy}}{{dx}}=\frac{{dy}}{{du}}×\frac{{du}}{{dx}} \\…
Question Number 142643 by ArielVyny last updated on 03/Jun/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{cos}^{\mathrm{2}} {t}}{{sint}}{dt} \\ $$ Answered by MJS_new last updated on 03/Jun/21 $$\int\frac{\mathrm{cos}^{\mathrm{2}} \:{t}}{\mathrm{sin}\:{t}}{dt}=\int\frac{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \:{t}}{\mathrm{sin}\:{t}}{dt}=\int\left(−\mathrm{sin}\:{t}\:+\mathrm{csc}\:{t}\right){dt}=…
Question Number 11567 by Nayon last updated on 28/Mar/17 $${why}\:\:\:\:\:\:{li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\:\frac{{f}\left({x}\right)}{{g}\left({x}\right)}={li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{f}'\left({x}\right)}{{g}'\left({x}\right)} \\ $$ Answered by mrW1 last updated on 28/Mar/17 $${l}'{hopital}'{s}\:{rule} \\ $$ Terms…
Question Number 77103 by Boyka last updated on 03/Jan/20 Commented by turbo msup by abdo last updated on 03/Jan/20 $${let}\:{I}=\int\:\:\frac{\mathrm{2}}{\mathrm{2}+{sinx}}{dx}\:{changement} \\ $$$${tan}\left(\frac{{x}}{\mathrm{2}}\right)\:={t}\:{give}\: \\ $$$${I}=\int\:\:\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }}×\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 142639 by ajfour last updated on 03/Jun/21 Commented by ajfour last updated on 03/Jun/21 $${Find}\:{maximum}\:{value}\:{of} \\ $$$$\:\left({AC}\right)\left({CD}\right)\left({DB}\right). \\ $$ Commented by mr W…
Question Number 11565 by Nayon last updated on 28/Mar/17 $${if}\:\frac{{dy}}{{dx}}={p}\:\:,{then}\:{why}\:{dy}={pdx}? \\ $$ Answered by mrW1 last updated on 28/Mar/17 $${if}\:\frac{{dy}}{{dx}}={p}\Rightarrow{y}={px} \\ $$$$\Rightarrow{dy}={pdx} \\ $$ Terms…
Question Number 11563 by Nayon last updated on 28/Mar/17 $${if}\:\:{f}\left({x}\right)={g}\left({y}\right) \\ $$$${then}\:{why}\:\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)=\frac{{d}}{{dy}}\left({g}\left({y}\right)\right)? \\ $$ Commented by mrW1 last updated on 28/Mar/17 $${this}\:{is}\:{not}\:{always}\:{correct}.\:{but} \\ $$$$\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)=\frac{{d}}{{dy}}\left({g}\left({y}\right)\right)×\frac{{dy}}{{dx}} \\…
Question Number 142629 by qaz last updated on 03/Jun/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{n}} \centerdot\frac{\mathrm{2n}−\mathrm{1}}{\left(\mathrm{2n}\right)!}\centerdot\left(\frac{\pi}{\mathrm{2}}\right)^{\mathrm{2n}} \\ $$$$=\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{2n}−\mathrm{1}}{\left(\mathrm{2n}\right)!}\centerdot\left(−\left(\frac{\pi}{\mathrm{2}}\right)^{\mathrm{2}} \right)^{\mathrm{n}} \\ $$$$=\left(\mathrm{2xD}−\mathrm{1}\right)\mid_{\mathrm{x}=\pi/\mathrm{2}} \underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} }{\left(\mathrm{2n}\right)!}…
Question Number 142630 by iloveisrael last updated on 03/Jun/21 $$\:{Given}\:{f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}^{{x}} } \\ $$$${find}\:{the}\:{value}\:{of} \\ $$$${f}\left(\frac{\mathrm{1}}{\mathrm{2018}}\right)×{f}\left(\frac{\mathrm{3}}{\mathrm{2018}}\right)×{f}\left(\frac{\mathrm{2015}}{\mathrm{2018}}\right)×{f}\left(\frac{\mathrm{2017}}{\mathrm{2018}}\right)=? \\ $$ Commented by MJS_new last updated on 03/Jun/21 $$\mathrm{no}\:“\mathrm{nice}''\:\mathrm{value}…
Question Number 142624 by Engr_Jidda last updated on 03/Jun/21 $${fine}\:{the}\:{equation}\:{and}\:{the}\:{corresponding} \\ $$$${sketch}\:{of}\:{graph}\:{of}\:{the}\:{imageof}\:{the} \\ $$$${straight}\:{line}\:{joining}\:\left(−\mathrm{1},−\mathrm{1}\right)\:{and} \\ $$$$\left(\mathrm{2},\mathrm{1}\right)\:{under}\:{the}\:{transformation}\:{equation} \\ $$$${w}=\left(\mathrm{2}+{i}\right){z} \\ $$ Terms of Service Privacy Policy…