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Please show your work or process.

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Solution

1)df/dx=df/du*du/dx+df/dv*dv/dx=(1+v^2)*e^x+(1+2uv)*y= =(1+x^2y^2)e^x+(1+2e^x*xy+2xy^2)y df/dy=df/du*du/dy+df/dv*dv/dy=(1+v^2)+(1+2uv)x =1+x^2y^2+(1+2e^x*xy+2xy^2)x 2) f=u+v+uv^2=e^x+y+xy+(e^x+y)x^2y^2 df/dx=e^x+y+e^x*x^2y^2+(e^x+y)2xy^2 which is equal with df/dx in 1) df/dy=1+x+x^2y^2+(e^x+y)2x^2y which is equal with df/dy in 1)