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Category: Differentiation

tan-3-x-sec-3-x-dx-

Question Number 138009 by bobhans last updated on 09/Apr/21 $$\int\:\mathrm{tan}\:^{\mathrm{3}} \left({x}\right)\:\sqrt{\mathrm{sec}\:^{\mathrm{3}} \left({x}\right)}\:{dx}\:=? \\ $$ Answered by EDWIN88 last updated on 09/Apr/21 $$\mathcal{E}\:=\:\int\:\mathrm{tan}\:^{\mathrm{3}} \left({x}\right)\:\mathrm{sec}\:\left({x}\right)\:\sqrt{\mathrm{sec}\:\left({x}\right)}\:{dx} \\ $$$$=\:\int\:\mathrm{tan}\:\left({x}\right)\mathrm{sec}\:\left({x}\right)\left(\mathrm{sec}\:^{\mathrm{2}}…

Question-137650

Question Number 137650 by bemath last updated on 05/Apr/21 Answered by bemath last updated on 05/Apr/21 $${By}\:{Langrange}\:{multiplier} \\ $$$${f}\left({x},{y},\lambda\right)=\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\lambda\left(\mathrm{6}{x}^{\mathrm{2}} +\mathrm{2}{xy}+\mathrm{6}{y}^{\mathrm{2}} −\mathrm{9}\right) \\ $$$$\frac{\partial{f}}{\partial{x}}\:=\:\mathrm{2}{x}+\lambda\left(\mathrm{12}{x}+\mathrm{2}{y}\right)=\mathrm{0}…

y-ln-3x-2-x-solve-y-6-x-

Question Number 72044 by 20190927 last updated on 23/Oct/19 $$\mathrm{y}=\mathrm{ln}\left(\mathrm{3x}^{\mathrm{2}} +\mathrm{x}\right)\:\:\:\mathrm{solve}\:\mathrm{y}^{\left(\mathrm{6}\right)} \left(\mathrm{x}\right) \\ $$ Commented by mathmax by abdo last updated on 24/Oct/19 $${we}\:{have}\:{y}^{'} \left({x}\right)=\frac{\mathrm{6}{x}+\mathrm{1}}{\mathrm{3}{x}^{\mathrm{2}}…