MATH 2D Study Guide - Quiz Guide: Directional Derivative, Scilab

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2D
• Professor: All

Document Summary

Problem 1. (5 points) let u = f (x, y, z) = 3xey sin(xz) with x = ln(t/2), y = t2 4, z = (1 t) 1. Compute du/dt and evaluate it at x = 0, y = 0, z = 1. Alternatively, we could substitute all expressions for x, y, and z in terms of t into u and take a normal derivative. Here, i will use the chain rule and partial derivatives: du dt. = (3ey z cos(xz)) dz dt. + (3xey) (2t) + ( x cos(xz)) (cid:0) 1(1 t) 2 ( 1)(cid:1) + 6txey x cos(xz) (1 t)2. Now, to evaluate at the given point, note that this point occurs exactly at t = 2. So, plug in x = 0, y = 0, z = 1, and t = 2: (cid:12)(cid:12)(cid:12)t=2 du dt. + 6 2 0 e0 0 cos(0 ( 1)) (1 2)2.