calculus

posted by robert

find the total differential of the function
f(x,y)= xye^(x+y)

  1. Steve

    df = ∂f/∂x dx + ∂f/∂y dy

    f = xye^(x+y)
    df = (ye^(x+y) + xye^(x+y)) dx + (xe^(x+y) + xye^(x+y)) dy
    = e^(x+y) [ (x+1)y dx + (y+1)x dy]

    or, separating the product a bit,

    f = xe^x * ye^y
    df = e^x(x+1)*ye^y dx + e^y(y+1)*xe^x dy
    = e^x*e^y [(x+1)y dx + (y+1)x dy]

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