Question and Answers Forum

All Questions      Topic List

Differentiation Questions

Previous in All Question      Next in All Question      

Previous in Differentiation      Next in Differentiation      

Question Number 93477 by Ar Brandon last updated on 13/May/20

$$\mathrm{Differentiate}\mathrm{completely};$$$$1\mathrm{\setminus }\mathrm{f}(\mathrm{x},\mathrm{y})={\mathrm{x}}^2+{\mathrm{xy}}^2+\mathrm{siny}$$$$2\mathrm{\setminus }\mathrm{f}(\mathrm{x},\mathrm{y})={\mathrm{e}}^{{\mathrm{x}}^2+{\mathrm{y}}^2}$$$$3\mathrm{\setminus }\mathrm{f}(\mathrm{x},\mathrm{y},\mathrm{z})=\tan (3\mathrm{x}-\mathrm{y})+6^{\mathrm{y}+2}$$

Answered by Rio Michael last updated on 13/May/20

$$\mathrm{partial}\mathrm{derivative}$$$$\frac{\partial f}{\partial x}=2x+y^2,\frac{\partial f}{\partial y}=2xy+\cos y$$

Commented by Ar Brandon last updated on 13/May/20

$$\mathrm{Hi}\mathrm{thanks}\mathrm{for}\mathrm{your}\mathrm{reply}.\mathrm{But}\mathrm{actually}$$$${\mathrm{I}}^{\prime }\mathrm{m}\mathrm{looking}\mathrm{for}\mathrm{the}\mathrm{total}\mathrm{derivative}.$$$$\mathrm{Do}\mathrm{you}\mathrm{have}\mathrm{an}\mathrm{idea}\mathrm{on}\mathrm{how}\mathrm{to}\mathrm{go}\mathrm{about}?$$

Answered by john santu last updated on 13/May/20

$$\left(1\right)\mathrm{let}\mathrm{z}=\mathrm{f}(\mathrm{x},\mathrm{y})={\mathrm{x}}^2+{\mathrm{xy}}^2+\sin \mathrm{y}$$$$\mathrm{dz}=\frac{\partial \mathrm{z}}{\partial \mathrm{x}}.\mathrm{dx}+\frac{\partial \mathrm{z}}{\partial \mathrm{y}}.\mathrm{dy}$$$$\mathrm{dz}=(2\mathrm{x}+{\mathrm{y}}^2)\mathrm{dx}+(2\mathrm{xy}+\cos \mathrm{y})\mathrm{dy}$$$$$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com