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Category: Differentiation

Question-167404

Question Number 167404 by bharath23 last updated on 15/Mar/22 Answered by alephzero last updated on 15/Mar/22 $$\frac{\partial{f}}{\partial{x}}\:=\:\frac{\partial}{\partial{x}}\left({y}\:\mathrm{cos}\:{xy}\right)\:=\:{y}\:\frac{\partial}{\partial{x}}\left(\mathrm{cos}\:{xy}\right) \\ $$$$=\:{y}\:\frac{\partial\left(\mathrm{cos}\:{xy}\right)}{\partial\left({xy}\right)}\:\centerdot\:\frac{\partial\left({xy}\right)}{\partial{x}}\:=\:−{y}^{\mathrm{2}} \:\mathrm{sin}\:{xy}\:\blacksquare \\ $$ Terms of Service…

Find-domain-and-range-of-the-function-f-x-x-2-6x-8-x-5-Also-draw-the-graph-

Question Number 36316 by ajfour last updated on 31/May/18 $${Find}\:{domain}\:{and}\:{range}\:{of}\:{the} \\ $$$${function}\:\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{8}}{{x}−\mathrm{5}}\:\:. \\ $$$${Also}\:{draw}\:{the}\:{graph}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 31/May/18 $${y}=\frac{{x}^{\mathrm{2}}…

Question-167301

Question Number 167301 by mnjuly1970 last updated on 12/Mar/22 Answered by amin96 last updated on 12/Mar/22 $$\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{8}}} \frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}\left(\mathrm{1}−\boldsymbol{\mathrm{cos}}\left(\frac{\pi}{\mathrm{4}}−\boldsymbol{\mathrm{x}}\right)\right)}\boldsymbol{\mathrm{dx}}\:\:\:\:\frac{\pi}{\mathrm{4}}−\boldsymbol{\mathrm{x}}=\boldsymbol{\mathrm{t}} \\ $$$$ \\ $$$$\boldsymbol{\mathrm{t}}\left[\frac{\pi}{\mathrm{8}};\:\frac{\pi}{\mathrm{4}}\right]\:\:\:\:\boldsymbol{{I}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\int_{\frac{\pi}{\mathrm{8}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\boldsymbol{\mathrm{dt}}}{\left(\mathrm{1}−\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{t}}\right)\right)}=\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{2}}}\int_{\frac{\pi}{\mathrm{8}}}…

Question-167267

Question Number 167267 by mnjuly1970 last updated on 11/Mar/22 Answered by mindispower last updated on 15/Mar/22 $${IBP}\Rightarrow\Omega=\left[{ln}\left(\mathrm{1}+{x}\right){Li}_{\mathrm{2}} \left(\mathrm{1}−{x}\right)\right]_{\mathrm{0}} ^{\mathrm{1}} −\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left(\mathrm{1}+{x}\right){ln}\left({x}\right)}{\mathrm{1}−{x}}{dx} \\ $$$$=−\int_{\mathrm{0}} ^{\mathrm{1}}…

let-f-x-arctan-x-y-calculate-2-f-x-2-x-y-2-f-y-2-x-y-2-f-x-y-x-y-2-f-y-x-x-y-

Question Number 36177 by prof Abdo imad last updated on 30/May/18 $${let}\:{f}\left({x}\right)=\:{arctan}\left(\frac{{x}}{{y}}\right) \\ $$$${calculate}\:\:\frac{\partial^{\mathrm{2}} {f}}{\partial{x}^{\mathrm{2}} }\left({x},{y}\right)\:,\:\frac{\partial^{\mathrm{2}} {f}}{\partial{y}^{\mathrm{2}} }\left({x},{y}\right),\:\frac{\partial^{\mathrm{2}} {f}}{\partial{x}\partial{y}}\left({x},{y}\right) \\ $$$$\frac{\partial^{\mathrm{2}} {f}}{\partial{y}\partial{x}}\left({x},{y}\right) \\ $$ Commented…