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Category: Differentiation

write-the-taylor-expansion-of-f-x-x-2-cos-x-at-x-1-then-f-5-x-at-x-1-

Question Number 162025 by mnjuly1970 last updated on 25/Dec/21 $$\:\:\:\: \\ $$$$\:\:\:{write}\:\:{the}\:{taylor}\:{expansion}\:{of}\:: \\ $$$$\:\:\:\:\:\:{f}\left({x}\right)=\:{x}^{\:\mathrm{2}} .\:{cos}\left({x}\right)\:\:\:\:{at}\:\:{x}=\mathrm{1} \\ $$$$\:\:\:\:{then}\:\:\:\:\:\:\:\:{f}^{\:\left(\mathrm{5}\:\right)} \left({x}\right)\:\:{at}\:\:{x}=\mathrm{1}\:\:? \\ $$$$ \\ $$ Terms of Service…

Suppose-y-8-dy-dx-4-amp-d-2-y-dx-2-x-1-2-Find-the-value-of-1-d-xy-dx-x-1-1-d-2-xy-dx-2-x-1-

Question Number 96467 by john santu last updated on 01/Jun/20 $$\mathrm{Suppose}\:\mathrm{y}\:=\:\mathrm{8}\:;\:\frac{{dy}}{{dx}}\:=\:\mathrm{4}\:\&\: \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:\mid_{{x}=\mathrm{1}} \:=\:−\mathrm{2}\:.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\left(\mathrm{1}\right)\:\frac{{d}\left({xy}\right)}{{dx}}\:\mid_{{x}=\mathrm{1}} \\ $$$$\left(\mathrm{1}\right)\frac{{d}^{\mathrm{2}} \left({xy}\right)}{{dx}^{\mathrm{2}} }\:\mid_{{x}=\mathrm{1}} \: \\ $$$$…

Given-z-xy-4y-2-x-2-4y-2-x-y-0-find-minimum-and-maximum-value-of-z-

Question Number 96306 by bemath last updated on 31/May/20 $$\mathrm{Given}\:\mathrm{z}\:=\:\frac{\mathrm{xy}−\mathrm{4y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{4y}^{\mathrm{2}} }\:,\:\mathrm{x},\mathrm{y}\neq\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{z}\: \\ $$ Commented by john santu last updated…

Question-161802

Question Number 161802 by femKaren last updated on 22/Dec/21 Answered by mr W last updated on 22/Dec/21 $${f}\left({x}\right)=\mathrm{cos}^{\mathrm{3}} \:{x}+\mathrm{sin}^{\mathrm{3}} \:{x} \\ $$$${f}'\left({x}\right)=−\mathrm{3}\:\mathrm{cos}^{\mathrm{2}} \:{x}\:\mathrm{sin}\:{x}+\mathrm{3}\:\mathrm{sin}^{\mathrm{2}} \:{x}\:\mathrm{cos}\:{x} \\…

differenciate-xsin-xcos-x-

Question Number 161750 by CM last updated on 22/Dec/21 $${differenciate}\:{x}\mathrm{sin}\:{x}\mathrm{cos}\:{x} \\ $$ Commented by cortano last updated on 22/Dec/21 $$\:{f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{2}}{x}\:\mathrm{sin}\:\mathrm{2}{x}\: \\ $$$$\:\frac{{df}}{{dx}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{sin}\:\mathrm{2}{x}+\mathrm{2}{x}\:\mathrm{cos}\:\mathrm{2}{x}\right) \\ $$$$\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}{x}+{x}\:\mathrm{cos}\:\mathrm{2}{x} \\…

find-a-particular-solution-to-the-equation-y-y-x-sin-y-x-with-original-condition-y-1-pi-2-

Question Number 96192 by 1549442205 last updated on 30/May/20 $$\mathrm{find}\:\mathrm{a}\:\mathrm{particular}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{y}'\:=\frac{\mathrm{y}}{\mathrm{x}}+\mathrm{sin}\frac{\mathrm{y}}{\mathrm{x}}\:\mathrm{with}\:\mathrm{original}\:\mathrm{condition} \\ $$$$\mathrm{y}\left(\mathrm{1}\right)=\frac{\pi}{\mathrm{2}} \\ $$ Commented by john santu last updated on 30/May/20 $$\mathrm{set}\:{v}\:=\frac{{y}}{{x}}\:\Rightarrow\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:{v}\:+{x}\:\frac{{dv}}{{dx}}\:…

what-are-critical-points-of-this-function-z-xy-5xy-2-10y-

Question Number 96185 by bemath last updated on 30/May/20 $$\mathrm{what}\:\mathrm{are}\:\mathrm{critical}\:\mathrm{points}\:\mathrm{of}\:\mathrm{this} \\ $$$$\mathrm{function}\:\mathrm{z}\:=\:\mathrm{xy}+\mathrm{5xy}^{\mathrm{2}} +\mathrm{10y} \\ $$ Answered by john santu last updated on 30/May/20 $$\left(\mathrm{1}\right)\:\frac{\partial\mathrm{z}}{\partial{x}}\:=\:{y}+\mathrm{5}{y}^{\mathrm{2}} \:=\:\mathrm{0}\:…