help me with the following exercises very kind with legible handwriting I would appreciate it thanks

a) From the following function answer the questions: f(x, y) = x yi + + (x + 4y + 4x)j 1- What is the derivative of the function at "x"? 2-What is the derivative of the function at "y"? 3- Explain what values the "x" must have so that the derivative at "i" is 0. Does the value of the "y" matter? 4- Explain what values "y" must have so that the derivative at "(" is 0. Does the value of x matter? 5-Explain what values "x" must have so that the derivative in "j" is 0. Does the value of y matter? 6- Explain what values "y" must have so that the derivative in "]" is 0. Does the value of x matter? 7- Is there a way to find the value of "x" and "y", which makes the derivatives at "i and "j' equal to 0? a) Work with the same function: fix, y) = xy +x+y+4 1- Obtain the definite integral of the function in "x" from 1 to 3: [ randx = [(y + +y+ 4)dx 2- Obtain the definite integral of the function in "y" from 2 to 4: [randy = [(xy + x +y+ 4)dy 3- Now the result of the section to integrate it in "and" from 2 to 4: 4- Now the result of part b integrate it into "x" from 1 to 3: [ [ ranardx = [[( + x + y+ 4 )dydx 5- Compare the results of part c and d. Are they the same or different? What are their differences