Question Number 82109 by jagoll last updated on 18/Feb/20 $${what}\:{is}\:{solution} \\ $$$$\frac{{dy}}{{dx}}\:=\:\mathrm{sin}\:\left({x}+{y}\right) \\ $$ Commented by mr W last updated on 18/Feb/20 $${u}={x}+{y} \\ $$$${y}={u}−{x}…
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Question Number 82059 by jagoll last updated on 18/Feb/20 $${what}\:{is}\:{derivative}\:{of}\:\:{h}\:=\:\sqrt{{ln}\left({x}\right)} \\ $$$${by}\:{first}\:{principle}\:{method}\: \\ $$ Answered by Henri Boucatchou last updated on 18/Feb/20 $$\frac{\mathrm{dh}\left(\mathrm{x}\right)}{\mathrm{dx}}=\frac{\mathrm{d}\sqrt{\mathrm{lnx}}}{\mathrm{dx}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\frac{\mathrm{dlnx}}{\mathrm{dx}}}{\mathrm{2}\sqrt{\mathrm{lnx}}}…
Question Number 82018 by TawaTawa last updated on 17/Feb/20 $$\mathrm{Differentiate}\:\:\:\:\:\mathrm{y}\:\:=\:\:\mathrm{2}^{\mathrm{x}} \:\:\:\:\mathrm{from}\:\mathrm{the}\:\mathrm{first}\:\mathrm{principle}. \\ $$ Commented by john santu last updated on 17/Feb/20 $${ln}\:{y}\:=\:{x}\:{ln}\:\mathrm{2} \\ $$$$\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{ln}\left({y}\right)\:\:=\:\underset{{h}\rightarrow\mathrm{0}}…
Question Number 81954 by Cmr 237 last updated on 16/Feb/20 $$\left.\:{soit}\:\alpha\in\right]\mathrm{0};\pi\left[.\:{determiner}:\right. \\ $$$$\left.\mathrm{1}\right){le}\:{module}\:{et}\:{l}'{argument}\:{de}: \\ $$$$\left.\boldsymbol{{a}}\left.\right)\mathrm{1}−\boldsymbol{{e}}^{\boldsymbol{{i}}\alpha} ,\boldsymbol{{b}}\right)\mathrm{1}+\boldsymbol{{e}}^{\boldsymbol{{i}\alpha}} \\ $$$$\left.\mathrm{2}\right)\boldsymbol{{deduire}}\:\boldsymbol{{le}}\:\boldsymbol{{module}}\:\boldsymbol{{et}}\:\boldsymbol{{l}}'\boldsymbol{{argument}}\:\boldsymbol{{de}} \\ $$$$\left.\:\left.\boldsymbol{{a}}\right)\:\frac{\mathrm{1}−\boldsymbol{{e}}^{\boldsymbol{{i}}\alpha} }{\mathrm{1}+{e}^{{i}\alpha} },\:{b}\right)\left(\mathrm{1}−{e}^{{i}\alpha} \right)\left(\mathrm{1}+{e}^{{i}\alpha} \right) \\…
Question Number 147474 by mnjuly1970 last updated on 21/Jul/21 Answered by mindispower last updated on 21/Jul/21 $$\frac{\mathrm{1}}{\mathrm{2}{a}}\left(\underset{{n}\geqslant−\infty} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}−{a}}−\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}+{a}}\right)=\underset{{n}\geqslant−\infty} {\sum}\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{16}{n}^{\mathrm{2}} −{a}^{\mathrm{2}} }={f}\left({a}\right)…
Question Number 147411 by mnjuly1970 last updated on 20/Jul/21 Answered by mnjuly1970 last updated on 20/Jul/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\overset{\sqrt{{x}}\::=\:{y}} {=}\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{2}{y}\:{dy}}{\mathrm{1}+{e}^{\:{y}} }\:=\mathrm{2}\:\int_{\mathrm{0}} ^{\:\infty} \frac{{ydy}}{\mathrm{1}+{e}^{\:{y}} } \\…
Question Number 81835 by M±th+et£s last updated on 15/Feb/20 Commented by M±th+et£s last updated on 15/Feb/20 $${hn}:\:{harmonic}\:{number} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 147355 by legand last updated on 20/Jul/21 Answered by ArielVyny last updated on 20/Jul/21 $${the}\:{question}\:{is}\:{not}\:{complete}\:{sir} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 147346 by mnjuly1970 last updated on 20/Jul/21 Answered by qaz last updated on 20/Jul/21 $$\mathrm{a}_{\mathrm{n}} =\mathrm{2}\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \left(\mathrm{1}−\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{n}} \mathrm{sin}\:\mathrm{xd}\left(\mathrm{sin}\:\mathrm{x}\right) \\ $$$$\Rightarrow\mathrm{a}_{\mathrm{n}} =\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}}…