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Category: Differentiation

z-x-2-y-3-dz-

Question Number 88179 by ubaydulla last updated on 08/Apr/20 $${z}={x}^{\mathrm{2}} /{y}^{\mathrm{3}} \:\:\:\:\:\:\:\:\:\:{dz}=? \\ $$ Answered by TANMAY PANACEA. last updated on 08/Apr/20 $${dz}=\left(\frac{\partial{z}}{\partial{x}}\right)_{{y}} {dx}+\left(\frac{\partial{z}}{\partial{y}}\right)_{{x}} {dy}…

Question-88029

Question Number 88029 by M±th+et£s last updated on 07/Apr/20 Answered by mind is power last updated on 08/Apr/20 $$−\mathrm{4}{sin}^{\mathrm{2}} \left(\mathrm{4}{x}\right)−\mathrm{8}{sin}\left(\mathrm{4}{x}\right)−\mathrm{9}{cos}^{\mathrm{2}} \left(\mathrm{4}{x}\right)+\mathrm{12}{cos}\left(\mathrm{4}{x}\right)−\mathrm{4}+\mathrm{6}{sin}\left(\mathrm{8}{x}\right) \\ $$$$=−\left(\mathrm{2}{sin}\left(\mathrm{4}{x}\right)−\mathrm{3}{cos}\left(\mathrm{4}{x}\right)+\mathrm{2}\right)^{\mathrm{2}} \\ $$$${f}\left({x}\right)=\frac{−\left(\mathrm{2}{sin}\left(\mathrm{4}{x}\right)−\mathrm{3}{cos}\left(\mathrm{4}{x}\right)+\mathrm{2}\right)^{\mathrm{2}}…

if-u-f-x-y-where-x-rcos-y-r-sin-prove-u-x-2-u-y-2-u-r-2-1-r-u-2-

Question Number 88015 by M±th+et£s last updated on 07/Apr/20 $${if}\:{u}={f}\left({x},{y}\right)\:{where}\:{x}={rcos}\left(\theta\right)\:\:,\:{y}={r}\:{sin}\left(\theta\right) \\ $$$${prove}\: \\ $$$$\left(\frac{\partial{u}}{\partial{x}}\right)^{\mathrm{2}} +\left(\frac{\partial{u}}{\partial{y}}\right)^{\mathrm{2}} =\left(\frac{\partial{u}}{\partial{r}}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{{r}}\left(\frac{\partial{u}}{\partial\theta}\right)^{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact:…

Question-22332

Question Number 22332 by A1B1C1D1 last updated on 15/Oct/17 Answered by ajfour last updated on 15/Oct/17 $$\frac{{d}\left[{f}\left({x}\right)\right]}{{dx}}=\mathrm{1}+\mathrm{2cos}\:{x}=\mathrm{0} \\ $$$$\Rightarrow\:\mathrm{cos}\:{x}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:{x}=\mathrm{2}{n}\pi\pm\frac{\mathrm{2}\pi}{\mathrm{3}}\:\:{where}\:{n}\in\mathbb{Z}\:. \\ $$$$\:\:\:\:{which}\:{is}\:{equivalent}\:{to} \\ $$$$\:\:\:\:{x}=\left(\mathrm{2}{n}+\mathrm{1}\right)\pi\pm\frac{\pi}{\mathrm{3}}\:.…

Solve-x-y-z-R-amp-x-y-z-K-Min-x-4-y-4-z-4-x-2-y-2-Source-Elementary-Ol

Question Number 153340 by mnjuly1970 last updated on 06/Sep/21 $$ \\ $$$$\:\:\:\:\:\mathrm{Solve}\:.. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}\:,\:\mathrm{y}\:,\:\mathrm{z}\:\in\:\mathbb{R}^{\:+} \:\&\:\:\mathrm{x}+\:\mathrm{y}=\:\mathrm{z} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{K}\::=\:\mathrm{Min}_{\:} \:\left(\frac{\:\mathrm{x}^{\:\mathrm{4}} \:+\:\mathrm{y}^{\:\mathrm{4}} +\:\mathrm{z}^{\:\mathrm{4}} }{\mathrm{x}^{\:\mathrm{2}} \mathrm{y}^{\:\mathrm{2}} }\:\right)\:=\:?\:\:\:\:\:\:\:\:\:\:\blacksquare\:\:\:\:\:\:\:\:\:…

Question-153252

Question Number 153252 by liberty last updated on 06/Sep/21 Answered by MJS_new last updated on 06/Sep/21 $${y}''=\mathrm{0} \\ $$$$\frac{\mathrm{2}{ax}\left({x}^{\mathrm{2}} −\mathrm{3}{b}\right)}{\left({x}^{\mathrm{2}} +{b}\right)^{\mathrm{3}} }=\mathrm{0} \\ $$$$\Rightarrow\:{x}=\mathrm{0}\vee{x}=\pm\sqrt{\mathrm{3}{b}}\vee{a}=\mathrm{0}\:\left(\mathrm{rejected}\right) \\…

Let-w-1-pi-n-n-N-a-n-p-0-n-1-2p-1-1-w-2p-1-and-b-n-p-0-n-1-n-1-w-p-Find-all-integer-n-such-as-a-n-b-n-

Question Number 87687 by ~blr237~ last updated on 05/Apr/20 $${Let}\:\:{w}=\left[\mathrm{1};\frac{\pi}{{n}}\right]\:,{n}\in\mathbb{N}^{\ast} \: \\ $$$$\:{a}_{{n}} =\underset{{p}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\:\frac{\mathrm{2}{p}+\mathrm{1}}{\mathrm{1}−{w}^{\mathrm{2}{p}+\mathrm{1}} }\:\:\:\:{and}\:\:\:{b}_{{n}} =\underset{{p}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\:\frac{{n}}{\mathrm{1}+{w}^{{p}} }\: \\ $$$${Find}\:\:{all}\:{integer}\:{n}\:{such}\:{as}\:\:{a}_{{n}} ={b}_{{n}} \:…