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: Find indicated nh order partial derivative: ap+qu 2. if u= (x – xo)P(y- yo)ª %3D

A: We will find the required partial derivative as following.

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: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Both first partial derivatives of the function f(x.y) are zero at the given points. Use the…

A:

Q: what is a and b please?

A: Use chain rule to find the h ' (x) and g ' (x).

Q: If a function is defined by an equation G(x,y)=0 and could be found explicitly as y=f(x), then the…

A: We have to check

Q: 2. Find the derivative of each of the following functions: y = x¹2 (i) (ii) (iii) (iv) y = 3x ¹ y =…

A: 1) y=x12Differentiate w.r.t.'x'dydx=ddx(x12)We know thatddx(xn)=nxn-1Thereforedydx=12x11

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: f (x, y) 3 6х + 3у — 7; Dif (x,y) a2f f(x,y) = 4x² – 3xy; %3D - дхду

A: We have to find the indicated partial derivative of this given functions .

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:

Q: When would you use a partial derivative? When you only need to differentiate half of a function. O…

A:

Q: Recall the derivatives of some common functions, and complete the table below Function Derivative…

A: