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Implicit Differentiation

  • Thread starter Icebreaker
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  • #1
Icebreaker
[tex]f(x,y,z,u,v)=xe^y+uz-\cos v=2[/tex]
[tex]g(x,y,z,u,v)=u\cos y+x^2v-yz^2=1[/tex]

I need to find [tex]u_z[/tex]. When I try to do it by implicitly differentiating and solving the equation, I get 2 contradictory answers. If I try the formula, i.e.

[tex]f_z + f_uu_z + f_vv_z = 0[/tex]
[tex]g_z + g_uu_z + g_vv_z = 0[/tex]

I get an answer, but I'm not sure if it's right, since it does not equal to the answer I get when I differentiate implicitly. Any help?

Also I'm not entirely sure if my "formula" is right. Maybe this formula is just implicit differentiation, I haven't looked into it.
 
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Answers and Replies

  • #2
Tom Mattson
Staff Emeritus
Science Advisor
Gold Member
5,500
7
2 things:

1. Please show how you started, and where you got stuck.

2. Please stop posting homework problems in the Math section. They should go in the Homework section.

Thanks.
 

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