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Category: Differentiation

calculus-x-y-z-R-and-x-2-y-2-z-2-1-find-min-x-y-z-R-yz-x-xz-y-xy-z-m-n-1970-

Question Number 116793 by mnjuly1970 last updated on 06/Oct/20 $$\:\:\:\:\:\:\:..{calculus}.. \\ $$$$\:\:{x},{y},{z}\:\in\mathbb{R}^{+} \:\:{and}\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:=\mathrm{1} \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{find}\:\:\:\:\:\: \\ $$$$\:\:\:\:{min}_{{x},{y},{z}\in\mathbb{R}^{+\:\:\:\:} } \left(\left(\frac{{yz}}{{x}}+\frac{{xz}}{{y}}+\frac{{xy}}{{z}}\right)\:\right)=? \\…

h-x-determinant-sin-x-cos-x-tan-x-cos-2x-sin-2x-tan-2x-x-3-1-4-x-4-xsin-x-h-0-

Question Number 182026 by cortano1 last updated on 03/Dec/22 $$\:\:\mathrm{h}\left(\mathrm{x}\right)=\:\begin{vmatrix}{\mathrm{sin}\:\mathrm{x}\:\:\:\:\:\mathrm{cos}\:\mathrm{x}\:\:\:\:\:\:\:\mathrm{tan}\:\mathrm{x}}\\{\mathrm{cos}\:\mathrm{2x}\:\:\mathrm{sin}\:\mathrm{2x}\:\:\:\:\:\mathrm{tan}\:\mathrm{2x}}\\{\:\:\:\mathrm{x}^{\mathrm{3}} \:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{4}}\mathrm{x}^{\mathrm{4}} \:\:\:\:\:\:\mathrm{xsin}\:\mathrm{x}}\end{vmatrix} \\ $$$$\:\:\mathrm{h}'\left(\mathrm{0}\right)\:=? \\ $$ Answered by SEKRET last updated on 03/Dec/22 $$\:\mathrm{0} \\…

Given-f-2-cos-2-2-sin-2-find-maximum-value-minimum-value-

Question Number 116433 by bemath last updated on 04/Oct/20 $$\mathrm{Given}\:\mathrm{f}\left(\theta\right)\:=\:\mathrm{2}^{\mathrm{cos}\:^{\mathrm{2}} \left(\theta\right)} \:+\:\mathrm{2}^{\mathrm{sin}\:^{\mathrm{2}} \left(\theta\right)} \\ $$$$\mathrm{find}\:\begin{cases}{\mathrm{maximum}\:\mathrm{value}}\\{\mathrm{minimum}\:\mathrm{value}}\end{cases} \\ $$ Answered by bobhans last updated on 04/Oct/20 $$\Rightarrow\:\mathrm{f}\left(\theta\right)\:=\:\mathrm{2}^{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}}…

Question-50834

Question Number 50834 by Tinkutara last updated on 21/Dec/18 Commented by ajfour last updated on 21/Dec/18 $${h}\left({x}\right)=\:\frac{\left({x}−\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} +\mathrm{2}}{{x}−\frac{\mathrm{1}}{{x}}}\:\:=\sqrt{\mathrm{2}}\left({z}+\frac{\mathrm{1}}{{z}}\right) \\ $$$$\:\:{where}\:\:\:{z}\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\left({x}−\frac{\mathrm{1}}{{x}}\right) \\ $$$$\Rightarrow\:\:{h}\left({x}\right)\mid_{{min}} \:=\:\mathrm{2}\sqrt{\mathrm{2}}\:. \\ $$…

If-z-x-2-tan-1-y-x-find-2-z-x-y-at-1-1-

Question Number 116319 by bemath last updated on 03/Oct/20 $$\mathrm{If}\:\mathrm{z}\:=\:\mathrm{x}^{\mathrm{2}} \:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{y}}{\mathrm{x}}\right),\:\mathrm{find}\:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{x}\partial\mathrm{y}}\: \\ $$$$\mathrm{at}\:\left(\mathrm{1},\mathrm{1}\right) \\ $$ Answered by john santu last updated on 03/Oct/20…