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Category: Differentiation

Question-167899

Question Number 167899 by peter frank last updated on 28/Mar/22 Answered by floor(10²Eta[1]) last updated on 29/Mar/22 $$\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{n}} =\mathrm{1}+\left(_{\mathrm{1}} ^{\mathrm{n}} \right)\mathrm{x}+\left(_{\mathrm{2}} ^{\mathrm{n}} \right)\mathrm{x}^{\mathrm{2}} +…+\left(_{\mathrm{r}−\mathrm{1}} ^{\mathrm{n}}…

If-x-2t-sin-2t-y-e-sin-2t-prove-that-1-y-dy-dx-tan-pi-4-t-

Question Number 102342 by bemath last updated on 08/Jul/20 $${If}\:\begin{cases}{{x}=\mathrm{2}{t}+\mathrm{sin}\:\mathrm{2}{t}}\\{{y}={e}^{\mathrm{sin}\:\mathrm{2}{t}} }\end{cases} \\ $$$${prove}\:{that}\:\frac{\mathrm{1}}{{y}}.\frac{{dy}}{{dx}}\:=\:\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}−{t}\right) \\ $$ Commented by Dwaipayan Shikari last updated on 08/Jul/20 $${There}\:{is}\:{some}\:{error}\:{in}\:{question}\:\:{if}\:\:\:{x}=\mathrm{2}{t}−{cos}\mathrm{2}{t}\:\:{then}\:{the}\:{prove}\:{is}\:{true} \\…

Question-102328

Question Number 102328 by bemath last updated on 08/Jul/20 Answered by bobhans last updated on 08/Jul/20 $$\left({ii}\right)\:{y}=\:\mathrm{2ln}\left(\frac{\sqrt{\mathrm{8}{x}−\mathrm{4}}}{{x}}\right)\:\Rightarrow{x}\:\geqslant\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${y}\:=\:\mathrm{ln}\left(\frac{\mathrm{8}{x}−\mathrm{4}}{{x}^{\mathrm{2}} }\right)\:\Rightarrow{e}^{{y}} .{x}^{\mathrm{2}} \:=\:\mathrm{8}{x}−\mathrm{4} \\ $$$${e}^{{y}} .{x}^{\mathrm{2}}…

Solve-this-linear-Equation-dy-dx-y-cos-x-1-2-sin-x-

Question Number 102323 by Learner101 last updated on 08/Jul/20 $${Solve}\:{this}\:{linear}\:{Equation} \\ $$$$\frac{{dy}}{{dx}}\:+\:{y}\:{cos}\:{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:{sin}\:{x} \\ $$ Answered by bemath last updated on 08/Jul/20 $${IF}\:\:{u}\left({x}\right)={e}^{\int\mathrm{cos}\:{x}\:{dx}} \:=\:{e}^{\mathrm{sin}\:{x}} \\ $$$${y}\left({x}\right)=\frac{\int\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:{x}\:{e}^{\mathrm{sin}\:{x}}…

dy-dx-8x-4y-2x-y-1-2-y-

Question Number 167838 by cortano1 last updated on 27/Mar/22 $$\:\:\:\:\:\:\frac{{dy}}{{dx}}=\mathrm{8}{x}+\mathrm{4}{y}+\left(\mathrm{2}{x}+{y}−\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:{y}=? \\ $$ Answered by mr W last updated on 27/Mar/22 $${let}\:{u}=\mathrm{2}{x}+{y}−\mathrm{1} \\ $$$$\frac{{du}}{{dx}}=\mathrm{2}+\frac{{dy}}{{dx}}…