Exact Equations

Author: John J Weber III, PhD Corresponding Textbook Sections:

Expected Educational Results

Review of Partial Derivatives

You may need to review:

Investigation 01

Let F(x,y)=xsin(y)+exy7y2+x5+4

Find the following first- and second-order partial derivatives:

Investigation 02

  1. Evaluate (sin(y)+yexy+5x4)dx

  2. Evaluate (xcos(y)+xexy14y)dy

  3. What is the constant of integration for each of the above integrals? Explain.

  4. What do you notice about the above results? Explain.

Total Differential

Definition: Total Differential

Recall from Calculus III:

Suppose some function F is dependent on two independent variables, x and y, more specifically, F(x,y)=C, where C is a constant. If F is differentiable, then the total differential is: dF=Fxdx+Fydy

Investigation 03

  1. Find the total differential of x2y+xsin(y)x+ey=7.

  2. Let Fx=M(x,y) and Fy=N(x,y).

  3. Find My

  4. Find Nx

  5. What do you notice about the above results? Explain.

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Last Modified: Wednesday, 2 September 2020 07:42 EDT