Mathematics
Juanita337
2015-11-04 10:47:33
Z=(x+y)ex,x=3t,y=2−t2, find dz/dt using the chain rule. assume the variables are restricted to domains on which the functions are defined.
ANSWERS
Shakita146
2015-11-04 11:57:43

[latex]z=(x+y)e^x[/latex] [latex]egin{cases}x=3t\y=2-t^2end{cases}[/latex] [latex]dfrac{mathrm dz}{mathrm dt}=dfrac{partial z}{partial x}dfrac{mathrm dx}{mathrm dt}+dfrac{partial z}{partial y}dfrac{mathrm dy}{mathrm dt}[/latex] [latex]dfrac{mathrm dz}{mathrm dt}=(e^x+(x+y)e^x)(3)+e^x(-2t)[/latex] [latex]dfrac{mathrm dz}{mathrm dt}=3(1+x+y)e^x-2te^x[/latex] [latex]dfrac{mathrm dz}{mathrm dt}=3(1+3t+2-t^2)e^{3t}-2te^{3t}[/latex] [latex]dfrac{mathrm dz}{mathrm dt}=3(3+t-t^2)e^{3t}[/latex]

ADD ANSWER