Differentials. Chain Rule Problem | Massachusetts Institute of Technology

University
Massachusetts Institute of Technology
Course
Multivariable Calculus
Pages

1

Academic year

2023
Author

Sporkz
Views

78

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:ArialMT;color:#000000;} .ft02{font-size:20px;font-family:CambriaMath;color:#000000;} .ft03{font-size:14px;font-family:CambriaMath;color:#000000;} .ft04{font-size:18px;line-height:23px;font-family:ArialMT;color:#000000;} .ft05{font-size:18px;line-height:22px;font-family:ArialMT;color:#000000;} Differentials. Chain Rule Problem In recitation, we will work on computing partial derivatives and the total differential ofa function. The function is x2 + y2, which depends on two variables, x and y. 𝑧 = 𝑥 2 + 𝑦 2 Now, the variables x and y themselves depend on two auxiliary variables, u and v. 𝑥 = 𝑢 2 − 𝑣 2 , 𝑦 = 𝑢𝑣 The setup is as follows: In Part A, we will compute the total differential dz in terms ofdx and dy. In Part B, we will compute partial z, partial u, in two different ways. We'llfirst compute the integral using the chain rule and then using total differentials.Substituting in some of the work we had done to solve that part.