(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[12] 3.Thetemperature T(x, y) at a point of the xy-plane is given by

T(x,y)= ye^(x^2).

A bug travels from left to right along the curve y = x^2

at a speed of 0.01m/sec. The bug

monitors T(x, y) continuously. What is the rate of change of T as the bug passes through

the point (1, 1)?

2. Relevant equations

Parameterizing x and y in terms of t, taking into account the velocity given (and assuming x and y are in meters, t is in seconds):

x = 0.01t

y = (0.01t)^2

t = 100 s

Chain rule

dT/dt = T_{x}dx/dt + T_{y}dy/dt

3. The attempt at a solution

dT/dt = 2xye^(x^2) * 0.01 + e^(x^2) * 0.02(0.01t) = 2*1*1*e * 0.01 + 0.02*e * 1 =

0.04*e degrees/sec

Right? Lol.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Chain Rule Problem

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