Question Number 90299 by zainal tanjung last updated on 22/Apr/20 $$\mathrm{help}\:\mathrm{me} \\ $$$$ \\ $$$$\mathrm{z}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{xy}.\mathrm{ln}\:\mathrm{xy} \\ $$$$\mathrm{z}_{\mathrm{x}} ^{'} =…?\:\:\:\mathrm{and}\:\:\mathrm{z}'_{\mathrm{y}} =…? \\ $$ Terms of Service…
Question Number 24733 by chernoaguero@gmail.com last updated on 25/Nov/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{second}\:\mathrm{derivative}\:\mathrm{of} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\sqrt{\mathrm{5x}+\mathrm{9}} \\ $$$$\mathrm{find}\:\mathrm{f}^{''} \\ $$ Commented by chernoaguero@gmail.com last updated on 25/Nov/17 $$\mathrm{Using}\:\mathrm{the}\:\mathrm{first}\:\mathrm{principle}\:\mathrm{method} \\…
Question Number 24680 by chernoaguero@gmail.com last updated on 24/Nov/17 Commented by mrW1 last updated on 24/Nov/17 Commented by chernoaguero@gmail.com last updated on 25/Nov/17 $$\mathrm{Thank}\:\mathrm{u}\:\mathrm{sir} \\…
Question Number 24598 by *D¬ B£$T* last updated on 22/Nov/17 $${if}\:{y}={x}^{\mathrm{3}} +{x}^{\mathrm{2}} +\mathrm{3}{x}…. \\ $$$${find}\:{its}\:{turning}\:{point} \\ $$ Answered by jota+ last updated on 23/Nov/17 $$\frac{{d}^{\mathrm{2}}…
Question Number 155477 by alcohol last updated on 01/Oct/21 Answered by puissant last updated on 01/Oct/21 $$\left.{a}\right)\:\forall{n}\in\mathbb{N},\:{f}\left({n}\right)={nf}\left(\mathrm{1}\right) \\ $$$$ \\ $$$${f}\left(\mathrm{2}\right)={f}\left(\mathrm{1}+\mathrm{1}\right)={f}\left(\mathrm{1}\right)+{f}\left(\mathrm{1}\right)=\mathrm{2}{f}\left(\mathrm{1}\right) \\ $$$${alors},\:{on}\:{montre}\:{par}\:{recurrence}\:{que} \\ $$$${f}\left({n}\right)={nf}\left(\mathrm{1}\right)..…
Question Number 155478 by alcohol last updated on 01/Oct/21 $$\underset{{k}\:=\:\mathrm{1}\:} {\overset{{n}} {\prod}}\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{{k}}\right)^{{k}} \:=\:{V}_{{n}} \\ $$$${find}\:{V}_{{n}} \\ $$ Answered by mindispower last updated on 01/Oct/21 $$…
Question Number 89805 by jagoll last updated on 19/Apr/20 $$\mathrm{find}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{with}\:\mathrm{constraint}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{1} \\ $$$$\mathrm{with}\:\mathrm{Lagrange}\:\mathrm{method} \\ $$ Commented by john santu…
Question Number 89753 by jagoll last updated on 19/Apr/20 $$\frac{\mathrm{d}}{\mathrm{dx}}\:\left(\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\mathrm{16}} {\prod}}\left(\mathrm{x}+\frac{\mathrm{1}}{\mathrm{k}}\right)\right)\underset{\:\mathrm{x}\:=\:\mathrm{0}} {\mid}\:=\:? \\ $$ Commented by mr W last updated on 19/Apr/20 $${sorry}!\:{i}\:{misread}\:\Pi\:{as}\:\Sigma. \\…
Question Number 155281 by mnjuly1970 last updated on 28/Sep/21 $$ \\ $$$$\:{f}\::\left[\:\mathrm{0}\:,\:\:\mathrm{6}\right]\:\rightarrow\:\left[−\mathrm{4}\:,\:\mathrm{4}\right] \\ $$$$\:\:\:{f}\:\left(\mathrm{0}\:\right)=\mathrm{0} \\ $$$$\:\:\:\:{f}\:\left(\mathrm{6}\:\right)=\mathrm{4}\: \\ $$$$\:\:{x},\:\:{y}\geqslant\mathrm{0}\:\:,\:{x}+{y}\:\leqslant\mathrm{6} \\ $$$$\:\:\:{f}\:\left({x}+{y}\:\right)=\frac{\mathrm{1}}{\mathrm{4}}\left\{{f}\left({x}\right)\sqrt{\mathrm{16}−\left({f}\left({y}\right)\right)^{\mathrm{2}} }\:+{f}\left({y}\right)\sqrt{\mathrm{16}−\left({f}\left({x}\right)\right)^{\mathrm{2}} }\:\right\} \\ $$$$\:\:\therefore\:\:\:\left(\:{f}\left(\mathrm{1}\right)\:+{f}\:\left(\mathrm{3}\right)\right)^{\:\mathrm{2}} =?…
Question Number 155237 by mnjuly1970 last updated on 27/Sep/21 $$ \\ $$$$\:\:\mathrm{I}{f}\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{ln}^{\:\mathrm{2}} \left({x}\:\right).{sin}\left(\sqrt{{x}\:}\:\right)}{{x}}\:{dx} \\ $$$$\:\:\:\:\:{prove}\:{that}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega\:=\:\mathrm{4}\:\gamma^{\:\mathrm{2}} \:+\:\frac{\pi^{\:\mathrm{3}} }{\mathrm{3}}\:\:\:\:\:\blacksquare\:{m}.{n} \\ $$ Answered by…