Question

Find the differential of the function l=xze^(-y^2-z^2)

Answer 1

`I=xze^(-y^2-z^2)`

`\mathrm dI=(\partial I)/(\partial x)\,\mathrm dx+(\partial I)/(\partial y)\,\mathrm dy+(\partial I)/(\partial z)\,\mathrm dz`

`\mathrm dI=ze^(-y^2-z^2)\,\mathrm dx-2yxze^(-y^2-z^2)\,\mathrm dy+\left(x-2xz^2\right)e^(-y^2-z^2)\,\mathrm dz`