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Category: Differentiation

Question-175275

Question Number 175275 by mnjuly1970 last updated on 25/Aug/22 Answered by Rasheed.Sindhi last updated on 25/Aug/22 $$\left(−\mathrm{5},\:{x}+\mathrm{2}{y}\right)\cup\left(\mathrm{2}{x}−{y}−\mathrm{4},\:\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\left(−\mathrm{5},{a}\right)\cup\left({a},\mathrm{3}\right) \\ $$$${a}={x}+\mathrm{2}{y}=\mathrm{2}{x}−{y}−\mathrm{4}=\frac{−\mathrm{5}+\mathrm{3}}{\mathrm{2}}=−\mathrm{1} \\ $$$${a}=−\mathrm{1} \\ $$$${x}+\mathrm{2}{y}=−\mathrm{1}\:\wedge\:\mathrm{2}{x}−{y}−\mathrm{4}=−\mathrm{1}…

y-x-x-x-dy-dx-

Question Number 109724 by bobhans last updated on 25/Aug/20 $$\:\:{y}\:=\:\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}\:\Rightarrow\:\frac{{dy}}{{dx}}\:?\: \\ $$ Answered by ajfour last updated on 25/Aug/20 $$\left({y}^{\mathrm{2}} −{x}\right)^{\mathrm{2}} ={x}+\sqrt{{x}} \\ $$$$\mathrm{2}\left({y}^{\mathrm{2}} −{x}\right)\left(\mathrm{2}{y}\frac{{dy}}{{dx}}−\mathrm{1}\right)=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}…

y-x-y-y-2-ln-x-u-y-1-u-y-y-2-y-y-2-x-y-1-ln-x-u-x-u-ln-x-u-1-x-u-ln-x-x-u-e-1-x-dx-ln-x-x-e-1-x-d

Question Number 175210 by mnjuly1970 last updated on 23/Aug/22 $$ \\ $$$$\:\:\:{y}'{x}\:+\:{y}\:=\:{y}^{\:\mathrm{2}} {ln}\left({x}\right) \\ $$$$\:\:\:\:{u}={y}^{\:−\mathrm{1}} \:\Rightarrow\:{u}'\:=−{y}'{y}^{\:−\mathrm{2}} \\ $$$$\:\:\:\:\:−{y}'{y}^{\:−\mathrm{2}} {x}\:−{y}^{−\mathrm{1}} =\:−{ln}\left({x}\right) \\ $$$$\:\:\:\:\:\:\:{u}'{x}\:−{u}\:=\:−{ln}\left({x}\right) \\ $$$$\:\:\:\:{u}'−\frac{\mathrm{1}}{{x}}\:{u}\:=\frac{−{ln}\left({x}\right)}{{x}}\: \\…

Question-44120

Question Number 44120 by peter frank last updated on 21/Sep/18 Answered by ajfour last updated on 21/Sep/18 $$\frac{{dy}}{{dx}}=\frac{{dy}/{d}\theta}{{dx}/{d}\theta}=\frac{{a}\mathrm{sin}\:\theta}{{a}+{a}\mathrm{cos}\:\theta}\:=\frac{\mathrm{sin}\:\theta}{\mathrm{1}+\mathrm{cos}\:\theta} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\left[\frac{{d}}{{d}\theta}\left(\frac{{dy}}{{dx}}\right)\right]/\left(\frac{{dx}}{{d}\theta}\right) \\ $$$$\:\:\:=\frac{\mathrm{cos}\:\theta\left(\mathrm{1}+\mathrm{cos}\:\theta\right)−\mathrm{sin}\:\theta\left(−\mathrm{sin}\:\theta\right)}{\left(\mathrm{1}+\mathrm{cos}\:\theta\right)^{\mathrm{2}} ×{a}\left(\mathrm{1}+\mathrm{cos}\:\theta\right)}…

Question-44091

Question Number 44091 by peter frank last updated on 21/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 22/Sep/18 $$ \\ $$$${ln}\left({y}+\mathrm{1}\right)\left\{\frac{\mathrm{2}\left({y}+\mathrm{1}\right)−{y}}{{y}\left({y}+\mathrm{1}\right)}\right\} \\ $$$${ln}\left({y}+\mathrm{1}\right)\left[\frac{\mathrm{2}}{{y}}−\frac{\mathrm{1}}{{y}+\mathrm{1}}\right] \\ $$$$ \\…