Calculate all four second-order partial derivatives of f (x, y) = sin (2xy)

Question

Isabelle Zamora

Mathematics

3 February, 01:16

Calculate all four second-order partial derivatives of f (x, y) = sin (2xy)

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Answers (1)

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Jairo Wallace · Answer 1

Z = sin (2xy) Ill use D for the partial differential sign

Dz/Dx = 2ycos (2xy)

Dz/Dy = 2xcos (2xy)

D^2z/Dx^2 = 2y.-2ysin (2xy) = - 4y^2sin (2xy)

D^2z/Dy^2 = - 4x^2sin (2xy)

D^2z/Dy. Dx = D/Dy (Dz/Dx) = 2y. - 2xsin (2xy) + 2. cos (2xy)

= - 4xysin (2xy) + 2 cos (2xy)

D^2z (Dx. Dy) is the same as the latter.