Using chain rule to obtain the derivative dz/dt

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Homework Help Overview

The discussion revolves around using the chain rule to find the derivative dz/dt, where z is a function of x and y, both of which are functions of t. The participants are exploring the application of the chain rule in this context.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to apply the chain rule and are sharing their calculations. There is a focus on verifying the correctness of their expressions for dz/dt, particularly in relation to the functions of x and y. Questions arise regarding the accuracy of their results compared to the teacher's answer.

Discussion Status

The discussion is ongoing, with participants seeking validation of their calculations and expressing uncertainty about their results in light of the teacher's posted answer. There is an indication of differing interpretations of the problem setup.

Contextual Notes

Some participants note that the teacher's function for x(t) is given as x(t) = 5t^4, which may influence the calculations and assumptions being made in the discussion.

catch22
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Homework Statement


upload_2015-11-2_22-26-2.png


Homework Equations


dz/dt = dz/dx⋅dx/dt + dz/dy⋅dy/dt

The Attempt at a Solution


[/B]
I am getting :

=[-sin(x+7y) ⋅ 10t] + [-sin(x+7y) ⋅ 7 ⋅ (-1/ t2)]

then changing x and y terms:

=[-sin((5t2)+7(1/t)) ⋅ 10t] + [-sin((5t2)+7(1/t)) ⋅ 7 ⋅ (-1/ t2)]
 
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catch22 said:

Homework Statement


View attachment 91274

Homework Equations


dz/dt = dz/dx⋅dx/dt + dz/dy⋅dy/dt

The Attempt at a Solution


[/B]
I am getting :

=[-sin(x+7y) ⋅ 10t] + [-sin(x+7y) ⋅ 7 ⋅ (-1/ t2)]

then changing x and y terms:

=[-sin((5t2)+7(1/t)) ⋅ 10t] + [-sin((5t2)+7(1/t)) ⋅ 7 ⋅ (-1/ t2)]

Do you have a question?
 
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Ray Vickson said:
Do you have a question?
yes, sorry, I'm just verifying If I had done it correctly.
the answer my teacher posted was :
upload_2015-11-2_23-20-31.png

which really got me questioning myself.
 
It seems that you teacher has ##x(t)=5t^4##
 
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