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Question Number 112310 by mohammad17 last updated on 07/Sep/20

Answered by bemath last updated on 07/Sep/20

$$\mathrm{Q}2/\mathrm{A})5\mathrm{x}+6\mathrm{y}=5\times 5+6\times 2$$$$5\mathrm{x}+6\mathrm{y}=37$$

Answered by mathmax by abdo last updated on 07/Sep/20

$${\mathrm{Q}}_1)\mathrm{i}\mathrm{suppose}\mathrm{the}\mathrm{question}\mathrm{is}\frac{\mathrm{dy}}{\mathrm{dx}}\mathrm{here}$$$$\mathrm{y}=\mathrm{cosx}{\tan }^3\mathrm{x}\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=-\mathrm{sinx}{\tan }^3\mathrm{x}+\mathrm{cosx}\left({3\tan }^2\mathrm{x}\right)(1+{\tan }^2\mathrm{x})$$$$=-\mathrm{sinx}{\tan }^3\mathrm{x}+{3\mathrm{cosxtan}}^2\mathrm{x}(1+{\tan }^2\mathrm{x})$$$$\mathrm{y}={\cos }^2\left(\frac{1}{\mathrm{x}}\right)\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=2\cos \left(\frac{1}{\mathrm{x}}\right)(-\frac{1}{{\mathrm{x}}^2}\sin \left(\frac{1}{\mathrm{x}}\right))=\frac{-2}{{\mathrm{x}}^2}\cos \left(\frac{1}{\mathrm{x}}\right)\sin \left(\frac{1}{\mathrm{x}}\right)$$

Answered by mathmax by abdo last updated on 07/Sep/20

$${\mathrm{Q}}_2)\det (\mathrm{A}\overrightarrow{\mathrm{M}},\overrightarrow{\mathrm{u}})=0\mathrm{with}\mathrm{A}(5,2)\mathrm{and}\overrightarrow{\mathrm{u}}(-6,5)\Rightarrow$$$$\left|\begin{array}{c}\mathrm{x}-5-6\\ \mathrm{y}-25\end{array}\right|=0\Rightarrow 5(\mathrm{x}-5)+6(\mathrm{y}-2)=0\Rightarrow$$$$5\mathrm{x}-25+6\mathrm{y}-12=0\Rightarrow 5\mathrm{x}+6\mathrm{y}-27=0$$

Answered by abdomsup last updated on 08/Sep/20

$$y^2=x^3+sin\left(xy\right)byderivation$$$$weget2{yy}^{{}^{\prime }}=3x^2+(y+{xy}^{{}^{\prime }})cos\left(xy\right)\Rightarrow$$$$2{yy}^{{}^{\prime }}-{xy}^{{}^{\prime }}cos\left(xy\right)=3x^2+ycos\left(xy\right)$$$$\Rightarrow (2y-xcos\left(xy\right))y^{{}^{\prime }}=3x^2+ycos\left(xy\right)$$$$\Rightarrow \frac{dy}{dx}=\frac{3x^2+ycos\left(xy\right)}{2y-xcos\left(xy\right)}$$$$$$

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