find the total derivative dz/dt, given:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]z=(x^2)-8xy-(y^3)[/tex] where [tex]x=3t[/tex] and [tex]y=1-t[/tex]

my steps look like this, can someone point out where i am going wrong, please?

[tex]z'=2x-8(x'y+y'x)-3y^2[/tex] where

[tex]x'=3[/tex] and [tex]y'=-1[/tex]

[tex]2(3t)-8[3(1-t)+(-1)(3t)]-3(1-t)^2[/tex]

[tex]=6t-8[3-3t+(-3t)]-3(1-2t+t^2)[/tex]

[tex]=6t-8(3-6t)-3(1-2t+t^2)[/tex]

[tex]=6t-24+48t-3+6t-3t^2[/tex]

[tex]=12t+48t-27-3t^2[/tex]

[tex]=-3t^2+60t-27[/tex]

however, the correct answer seems to be:

[tex]3t^2+60t-21[/tex]

i'm going nuts trying to figure out where i went wrong. please help.

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# Error computing total derivative

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