Business I / Partial Derivatives
Practice question · Select all that apply

For f(x,y)=x2y+eyf(x,y) = x^2 y + e^y, which are correct?

Hints
  1. Compute each partial in turn, holding the other variable constant.
  2. Check the mixed partial carefully, differentiate the first result again.
Show the answer
  • A. fx=2xyf_x = 2xy
  • B. fxx=2yf_{xx} = 2y
  • D. fy=x2+eyf_y = x^2 + e^y
Why

fx=2xyf_x = 2xy, fy=x2+eyf_y = x^2 + e^y, fxx=2yf_{xx} = 2y. But fxy=∂(2xy)/∂y=2xf_{xy} = \partial(2xy)/\partial y = 2x, not 2y2y.

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