Please find the secondorder partial derivative of the follow

Please find the second-order partial derivative of the following function..f(x, y) = y2 ex + 3y

Solution

df/dx = y²e^x+3y [Assuming y constant ]
Hence d²f/dx² = y²e^x+3y[Assuming y constant]

df/dy = 2ye^x+3y + y²3*e^x+3y = y(3y + 2)e^x+3y
Hence d²f/dy² = 2e^x+3y + 6ye^x+3y + 6ye^x+3y + 9y²e^x+3y =(9y² + 12y + 1) e^x+3y

And d²f/dydx = 2ye^x+3y + 3y²e^x+3y = y(3y + 2)e^x+3y

Hence the second order partial derivatives for f are:

d²f/dx² = y²e^x+3y
d²f/dy² = (9y² + 12y + 1) e^x+3y
d²f/dydx = y(3y + 2)e^x+3y