Partial Derivative Calculations for 2xy + 4yz + 5xz with Chain Rule

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Homework Help Overview

The discussion revolves around calculating partial derivatives of the function w = 2xy + 4yz + 5xz using the chain rule, with specific variable substitutions provided. The original poster shares their attempt at finding the derivative with respect to t after substituting values for s and t.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of the chain rule and the correct substitution of variables. Questions arise regarding the interpretation of the variable y and its substitution, as well as the accuracy of the terms in the function.

Discussion Status

Some participants have offered clarifications regarding the variable substitutions and identified potential errors in the original poster's calculations. There is an ongoing exploration of the correct terms and their implications for the derivative calculation.

Contextual Notes

Participants are addressing specific substitutions and potential misinterpretations of the function's terms, which may affect the overall calculations. The original poster's values for s and t are fixed, but there is uncertainty regarding the correct interpretation of y.

olivia333
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Homework Statement



w = 2xy + 4yz + 5xz
x = st
y = 3^(st)
z = t^2

s=5
t=1

Homework Equations



Chain rule: xy = x*y' + y*x'

The Attempt at a Solution



w = 2stest + 4test + 5st3

(partial derivatives) dw/dt = 2s2test + 2sest + 4tsst + 4est + 15st2

(partial derivatives) dw/dt (5,1) = 2(5)2e5 + 2*5e5 + 20e5 + 4e5 + 75

= 84e5+75

This is not correct. What did I mess up on? Thanks!
 
Last edited:
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When you said, y = 3^(st), did you mean y = e^(st)?
 
Yes I did mean that, but I actually figured out what I did wrong. I subbed in a y as t and not t^2.
 
Your 4yz term is not correct.

EDIT: Yep, beat me to it.
 

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