Question Number 83209 by ~blr237~ last updated on 28/Feb/20 $$\:\:\:{Prove}\:{that}\:\:\forall\:\:{x}\neq\frac{\pi}{\mathrm{4}}\:\:\:,\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\prod}}\left(\frac{{cos}\left(\frac{{x}}{\mathrm{2}^{{n}} }\right)+{cos}\left(\frac{\pi−\mathrm{2}{x}}{\mathrm{2}^{{n}+\mathrm{1}} }\right)}{\mathrm{2}}\:\right)\:=\:\frac{\mathrm{4}{cos}\mathrm{2}{x}}{\pi\left(\pi−\mathrm{4}{x}\right)}\: \\ $$ Answered by mind is power last updated on 28/Feb/20…
Question Number 83189 by john santu last updated on 28/Feb/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{3}\:^{\mathrm{rd}} \:\mathrm{derivative}\:\mathrm{of}\: \\ $$$$\mathrm{x}^{\mathrm{5}} \:\mathrm{ln}\left(\mathrm{2x}\right)\:\mathrm{using}\:\mathrm{the}\:\mathrm{Leibniz}\:\mathrm{theorem} \\ $$ Commented by jagoll last updated on 28/Feb/20 $$\mathrm{y}\:=\:\mathrm{x}^{\mathrm{5}}…
Question Number 17634 by tawa tawa last updated on 08/Jul/17 $$\mathrm{y}\:=\:\mathrm{x}!\:\:,\:\:\:\:\:\mathrm{Find}\:\:\:\mathrm{y}' \\ $$ Answered by alex041103 last updated on 09/Jul/17 $${Because}\:{x}!\:{is}\:{defined}\:{only}\:{for}\:{non}−{negative} \\ $$$${integers},\:{i}.{e}.\:{the}\:{function}\:{isn}'{t}\:{continious} \\ $$$${we}\:{cannot}\:{intagrate}\:{or}\:{diferentiate}\:{it}.…
Question Number 83156 by 09658867628 last updated on 28/Feb/20 $${find}\:{the}\:{derivtive}\:{of}\:{y}={e}^{\mathrm{cos}\:{x}} \\ $$ Commented by niroj last updated on 28/Feb/20 $$\:\:\:\mathrm{y}=\:\mathrm{e}^{\mathrm{cos}\:\mathrm{x}} \\ $$$$\:\:\mathrm{D}.\mathrm{w}.\mathrm{r}.\mathrm{to}\:\mathrm{x}. \\ $$$$\:\:\frac{\mathrm{dy}}{\mathrm{dx}}=\:\mathrm{e}^{\mathrm{cos}\:\mathrm{x}} \left(−\mathrm{sin}\:\mathrm{x}\right)…
Question Number 83149 by 09658867628 last updated on 28/Feb/20 $${y}={e}^{\mathrm{tan}{t}\:} \\ $$ Commented by Kunal12588 last updated on 28/Feb/20 $${what}\:{is}\:{the}\:{QUESTION}\:? \\ $$ Commented by Kunal12588…
Question Number 148676 by bemath last updated on 30/Jul/21 $$\mathrm{Find}\:\mathrm{local}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{function} \\ $$$$\:\mathrm{H}\left(\mathrm{x}\right)=\frac{\mathrm{34}}{\mathrm{3}+\frac{\mathrm{2x}}{\mathrm{x}^{\mathrm{2}} +\mathrm{3x}+\mathrm{1}}}\:. \\ $$ Answered by EDWIN88 last updated on 30/Jul/21 $${H}\left({x}\right)=\frac{\mathrm{34}{x}^{\mathrm{2}} +\mathrm{102}{x}+\mathrm{34}}{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{11}{x}+\mathrm{3}}…
Question Number 83139 by ~blr237~ last updated on 28/Feb/20 $${let}\:\:\:{c}_{\mathrm{0}} \:>\mathrm{0}\:\:{and}\:\:\forall\:{n}\in\mathbb{N}\:\:{c}_{{n}+\mathrm{1}} =\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\left({c}_{{n}} +\frac{\mathrm{1}}{{c}_{{n}} }\:\right)\:}\:\:\: \\ $$$${Explicit}\:\:{c}_{{n}} \:{in}\:{term}\:{of}\:{n}\:{and}\:\:{c}_{\mathrm{0}} \:\: \\ $$ Terms of Service Privacy Policy…
Question Number 83131 by 09658867628 last updated on 28/Feb/20 $${y}=\boldsymbol{{x}}^{\mathrm{4ln}\:\boldsymbol{{x}}} \\ $$ Commented by mr W last updated on 28/Feb/20 $${dear}\:{sir}: \\ $$$${please}\:{stop}\:{posting}\:{the}\:{same}\:{questions} \\ $$$${more}\:{times}!\:{if}\:{it}\:{occurs}\:{by}\:{mistake},…
Question Number 83127 by jagoll last updated on 28/Feb/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{x}\sqrt{\mathrm{3}}\:+\mathrm{y}\: \\ $$$$\mathrm{if}\:\mathrm{x}^{\mathrm{2}} \:+\mathrm{y}^{\mathrm{2}} −\mathrm{xy}=\:\mathrm{3}\:? \\ $$ Answered by mr W last updated on 28/Feb/20 $${let}\:{u}=\sqrt{\mathrm{3}}{x}+{y}…
Question Number 83042 by ~blr237~ last updated on 27/Feb/20 $${let}\:\:{a},{b}\:{two}\:{positive}\:{reals}\:{such}\:{as}\:\:{a}^{\mathrm{2}} −{b}^{\mathrm{2}} ={ab} \\ $$$${Explicit}\:\:\:{f}\left({a},{b}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{du}}{\:\sqrt{{a}+{bsin}^{\mathrm{2}} {u}}}\: \\ $$ Commented by mathmax by abdo last…