1. Home
  2. >Calculus 3
  3. >Partial Derivatives
Help

Differentials of multivariable functions

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

0/3
?
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
0/4
?
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}

          Topic Notes
          ?
          Notes:

          Differentials of 2 Variable Functions
          Suppose there is a 2-variable function z=f(x,y)z=f(x,y). Then we say that the differential dzdz is:

          dz=fxdx+fydydz = f_xdx + f_ydy


          Differentials of 3 Variable Functions
          Of course, differentials can be extended to 3-variable functions as well. Suppose there is a 3-variable function w=g(x,y,z)w=g(x,y, z). Then we say that the differential dwdw is:

          dw=gxdx+gydy+gzdzdw = g_x dx + g_y dy + g_z dz