For each part of this problem, state whether or not it is possible for a function f of two variables with continuous second partial derivatives to satisfy the given conditions. If it's possible, find such a function f; if it's not possible, explain why. af (a) fe sin(y), cos(x) ду af sin(x), af (b) = cos (y) dy

Q: Find each partial derivative: g(x,y,z) = 4xyz² - 3x

A: Step 1:    Step 2: Step 3: Step 4:

Q: Consider the function: Which of the following is a partial derivative of this function? x* - Bxy + z…

A: The given function is:f(x, y)=3xye8x2-8xy+12y2

Q: z = x3 – xy? + 3y2

A: Let us consider the two variable function z=f(x,y) The first partial derivative of the function is…

Q: Find the partial derivative. xev10ry Əx

A:

Q: Write a chain rule formula for the following derivative. dw for w f(p,q); p= g(x,), q = h(,) O A. aw…

A:

Q: Differentiate the function. ((5y + 1)3 Vy2 + 1 G(y) = In G'(y) =

A: Solve the following question

Q: 2. Find the anti-derivative of a. f(x) = 2x¹ - 5√√x³7−2e* ++ 3 1 1+x²

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Let w(z, y, z) = 1 + y² + z?, where z = 3', y = Int, and z = = et. Find I using the Chain Rule.

A:

Q: Find the first partial derivatives of the function. x³ - y6 fx = fy f(x, y) = +3 to x⁹ + y8

A: We have

Q: Q2n: Find the second order partial derivative of

A: