Question Number 84442 by Power last updated on 13/Mar/20 Answered by john santu last updated on 13/Mar/20 $$\mathrm{let}\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{3x}^{\mathrm{5x}} } \:\Rightarrow\mathrm{ln}\left(\mathrm{y}\right)=\:\mathrm{ln}\left(\mathrm{x}^{\mathrm{3x}^{\mathrm{5x}} } \right) \\ $$$$\mathrm{let}\:\mathrm{3x}^{\mathrm{5x}} \:=\:\mathrm{g}\left(\mathrm{x}\right)…
Question Number 18906 by Arnab Maiti last updated on 01/Aug/17 $$\mathrm{calculate}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:\:\mathrm{where}\: \\ $$$$\mathrm{y}=\mathrm{cos}^{−\mathrm{1}} \frac{\mathrm{a}+\mathrm{b}\:\mathrm{cosx}}{\mathrm{b}+\mathrm{a}\:\mathrm{cosx}}\:\left(\mathrm{b}>\mathrm{a}\right) \\ $$ Answered by ajfour last updated on 01/Aug/17 $$\:\mathrm{y}=\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{a}+\mathrm{bcos}\:\mathrm{x}}{\mathrm{b}+\mathrm{acos}\:\mathrm{x}}\right)…
Question Number 18905 by Arnab Maiti last updated on 01/Aug/17 $$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{differentiation} \\ $$$$\mathrm{of}\frac{\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }−\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }+\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\:\mathrm{with}\:\mathrm{respect} \\ $$$$\mathrm{to}\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }\:\:\mathrm{is}\:\:\frac{\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }}{\mathrm{x}^{\mathrm{6}} } \\ $$ Terms…
Question Number 84327 by sahnaz last updated on 11/Mar/20 $$\int\frac{\mathrm{3}−\mathrm{7u}}{\mathrm{7u}^{\mathrm{2}} −\mathrm{7}}\mathrm{du} \\ $$ Answered by 20092104 last updated on 15/Mar/20 $$\int\frac{\mathrm{3}−\mathrm{7}{u}}{\mathrm{7}{u}^{\mathrm{2}} −\mathrm{7}}{du} \\ $$$$=\int\frac{\mathrm{3}−\mathrm{7}{u}}{\mathrm{7}\left({u}^{\mathrm{2}} −\mathrm{1}\right)}{du}…
Question Number 84326 by sahnaz last updated on 11/Mar/20 $$\int\frac{\mathrm{3}−\mathrm{7u}}{\mathrm{7u}^{\mathrm{2}} −\mathrm{7}}\mathrm{du} \\ $$ Answered by TANMAY PANACEA last updated on 11/Mar/20 $$\frac{\mathrm{3}}{\mathrm{7}}\int\frac{{du}}{\left({u}+\mathrm{1}\right)\left({u}−\mathrm{1}\right)}−\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{d}\left(\mathrm{7}{u}^{\mathrm{2}} −\mathrm{7}\right)}{\mathrm{7}{u}^{\mathrm{2}} −\mathrm{7}} \\…
Question Number 149805 by mnjuly1970 last updated on 07/Aug/21 Answered by Ar Brandon last updated on 07/Aug/21 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{csc}^{\mathrm{2}} {x}\mathrm{ln}\left(\mathrm{1}+\mathrm{2sin}^{\mathrm{2}} {x}\right){dx} \\ $$$$\begin{cases}{{u}\left({x}\right)=\mathrm{ln}\left(\mathrm{1}+\mathrm{2sin}^{\mathrm{2}} {x}\right)}\\{{v}'\left({x}\right)=\mathrm{csc}^{\mathrm{2}}…
Question Number 84236 by niroj last updated on 10/Mar/20 $$\:\:\mathrm{If}\:\boldsymbol{\mathrm{ax}}^{\mathrm{2}} +\mathrm{2}\boldsymbol{\mathrm{hxy}}\:+\boldsymbol{\mathrm{by}}^{\mathrm{2}} =\:\mathrm{1},\:\mathrm{show}\:\mathrm{that} \\ $$$$\:\:\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:=\:\frac{\boldsymbol{\mathrm{h}}^{\mathrm{2}} −\boldsymbol{\mathrm{ab}}}{\left(\boldsymbol{\mathrm{hx}}+\boldsymbol{\mathrm{by}}\right)^{\mathrm{3}} }. \\ $$ Answered by TANMAY PANACEA last…
Question Number 84213 by jagoll last updated on 10/Mar/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{n}^{\mathrm{th}} \: \\ $$$$\mathrm{derivative}\:\mathrm{of}\:\:\mathrm{sin}\:^{\mathrm{5}} \left(\mathrm{x}\right)\:\mathrm{by}\:\mathrm{De}\:\mathrm{Moivre}'\mathrm{s} \\ $$$$\mathrm{formula} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 84178 by www.abhisheksoni39@gmail.com last updated on 10/Mar/20 $$\mathrm{Find}\:\frac{{dy}}{{dx}}\:\mathrm{given}\:\mathrm{that}\:{y}\:=\:\left({sin}^{{n}} \:{x}\:{cosnx}\right) \\ $$ Answered by john santu last updated on 10/Mar/20 $$\mathrm{using}\:\mathrm{product}\:\mathrm{rule} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{nsin}^{\mathrm{n}−\mathrm{1}} \left(\mathrm{x}\right)\:\mathrm{cos}\:\left(\mathrm{x}\right)\mathrm{cos}\:\left(\mathrm{nx}\right)+…
Question Number 149667 by mnjuly1970 last updated on 06/Aug/21 $$\: \\ $$$${f}\:\left({x}\:\right)=\:\frac{\mathrm{1}}{\:\sqrt{\:\mathrm{1}\:+\:{sin}\:\left({x}\:\right)}\:+\sqrt{\:\mathrm{1}\:+\:{cos}\:\left({x}\right)}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{find}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Min}\left(\:{f}\:\left({x}\right)\right)\:=? \\ $$$$ \\ $$ Answered by iloveisrael last updated…