Find all the second order partial derivatives of the given function.f(x, y) = cos xy2

Question

A. f_xx(x, y) = y² sin xy²; f_yy(x, y) = 2[2y² cos (xy²) - sin (xy²)] ; f_yx(x, y) = f_xy(x, y) = 2y[y² cos (xy²) - sin (xy²)]
B. f_xx(x, y) = -y⁴ cos xy²; f_yy(x, y) = - 2x[2xy² cos (xy²) + sin (xy²)]; f_yx(x, y) = f_xy(x, y) = - 2y[xy² cos (xy²) + sin (xy²)];
C. f_xx(x, y) = - y² sin xy²; f_yy(x, y) = 2[ sin (xy²)- 2y² cos (xy²)] ; f_yx(x, y) = f_xy(x, y) = 2y [sin (xy²)-y² cos (xy²)]
D. f_xx(x, y) = - y² sin xy²; f_yy(x, y) = 2y; f_yx(x, y) = f_xy(x, y) = 2

Answer 1

Answer: B