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Differentials of multivariable functions

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Intros
Lessons
  1. Differentials of Multivariable Functions Overview:
  2. A Review of Differentials
    • dy,dxdy, dx are differentials
    • dy=f′(x)dxdy=f'(x)dx
  3. Differentials of 2 Variable Functions
    • Differential dzdz
    • dz=fxdx+fydydz=f_xdx+f_ydy
    • An example
  4. Differentials of 3 Variable Functions
    • Differential dw dw
    • dw=gxdx+gydy+gzdzdw=g_xdx+g_ydy+g_zdz
    • An example
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Examples
Lessons
  1. Finding Differentials of 2 Variable Functions
    Compute the differential for the following function:

    f(x,y)=ex3+y3sin⁡x2f(x,y) = e^{x^3+y^3} \sin \frac{x}{2}

    1. Compute the differential for the following function:

      z=ln(x2y32)z = ln (\frac{x^2 y^3 }{2} )

      1. Finding Differentials of 3 Variable Functions
        Compute the differentials for the following function:

        g(x,y,z)=tan⁡[ln⁡(xy2z3)]g(x,y,z) = \tan [ \ln (xy^2 z^3) ]

        1. Compute the differentials for the following function:

          g=exyxy2z2g = \frac{e^{xy}}{xy^2z^2}