part a:
z^2+z*x*sin(x*y)+x^3*y=0
taking derivative w.r.t. x,
2*z*(dz/dx)+x*sin(x*y)*(dz/dx)+z*sin(x*y)+z*x*cos(x*y)*y+3*x^2*y=0
==>(dz/dx)*(2*z+x*sin(x*y))=-(z*sin(x*y)+z*x*cos(x*y)*y+3*x^2*y)
==>dz/dx=-(z*sin(x*y)+z*x*cos(x*y)*y+3*x^2*y)/(2*z+x*sin(x*y))
z^2+z*x*sin(x*y)+x^3*y=0
taking derivative w.r.t. y,
2*z*(dz/dy)+(dz/dy)*x*sin(x*y)+z*x*cos(x*y)*x+x^3=0
==>dz/dy=-(z*x*cos(x*y)*x+x^3)/(2*z+x*sin(x*y))
part b:
df/du=(df/dx)*(dx/du)+(df/dy)*(dy/du)
at u=-1 and v=1
x=v-u=2
y=u^2+v^2=2
df/dx=3*x^2*y
==>df/dx=3*2^2*2=24
df/dy=x^3
==>df/dy=x^3=2^3=8
dx/du=-1
dy/du=2*u=-2
then df/du=24*(-1)+8*(-2)
=-40
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please help with these questions
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