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

Question

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

Answer 1

Answer: C