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Find the gradient of f(x, y)?

Find the gradient of f(x, y)=xe^xy^2+cosy^2.

Answer: <e^xy^2+xy^2*e^xy^2, 2x^2*y*e^xy^2-2ysiny^2>

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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
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∂f/∂x = x'x e^(xy^2) + x(e^xy^2)'x = e^xy^2+xy^2*e^(xy^2)

∂f/∂y = x(e^xy^2)'y + (cosy^2)'y = 2x^2 y (e^xy^2) - 2y sin(y^2)

 

∇f

= <∂f/∂x, ∂f/∂y>

= <e^xy^2+xy^2*e^(xy^2), 2x^2 y (e^xy^2) - 2y sin(y^2)>