A function f is called homogeneous of degree n if it satisfies the equation f(tx, ty) = tnf(x, y) for all t, where n is a positive integer and f has continuous second-order partial derivatives. If f is homogeneous of degree n, show that fx(tx, ty) = tn − 1fx(x, y). (Hint: Use Chain Rule)

Q: Find all the first and second order partial derivatives of f(x, y) = 3 sin(2x + y) — 7 cos(x — y).…

A:

Q: Compute the first-order partial derivatives of the function z = 5х — у (Give exact answers. Use…

A:

Q: Give an example of ANY one nonlinear (i.e. powers of r, y can't just be 1) function z f(r, y) such…

A:

Q: Let be a function that allows continuous second partial derivatives, we know that: Vf(x, y) = (16x³…

A:

Q: Let f be a function admitting continuous second partial derivatives such that Vf(x, y) = (ax² – x,…

A: Solution :-

Q: Find all the second order partial derivatives of the given function. 10) f(x, y) = (x2 + y2)7

A:

Q: Let ƒ (x, y) = x³ − x² − 8x + 2xy − - - 12y². (a) Compute all first order and second order partial…

A:

Q: Find the nine second partial derivatives. w = x²y3+9xyz - 2yz W XX E W xy || = W XZ = Wyx Wyy Wyz =…

A:

Q: Show that the mixed partial derivatives Fxyy, Fyxy, and Fyyx  of F(x,y,z) = 2z / (x+y) are/aren’t…

A:

Q: ztg(x+y+z)- = 0

A:

Q: If f(x, y, z) = 2x5 + 3y5- 8x2y?z?, what is the partial derivative of f with %3D respect to z? fz =…

A:

Q: ompute the partial derivative: (1, y) = cos(x+ – 6y) -(0, т) —

A:

Q: Let be a function that allows continuous second partial derivatives, we know that: Vf(x,y) = (16x³ -…

A:

Q: Find the nine second partial derivatives. w = x²y3+9xyz - 2yz W XX E W xy || = W XZ = Wyx Wyy Wyz =…

A: First, we need to calculate the first partial derivatives of the function w = x²y³ + 9xyz - 2yz with…

Q: For the function f (x,y,z,w) with x, y, z, and w all functions of s, t, andr, write out the chain…

A: The function is fx,y,z,w x,y,z,w are functions of s,t,r.   Partial derivative of a function with…

Q: Find the first partial derivatives of f(x, y, z) af A. (5,5,-2) = B. of (5,5,-2) მყ = C. (5,5,-2) =…

A:

Q: 10.J Compute the matrix of partial derivatives of: f(x,y) = (x+y, x-y, xy) d.) f(x, y, z) =…

A:

Q: Find the maximum value of f(x1,2,,xn) = (x₁ - x₂ ... n)¹/" where x₁,..., In are positive numbers and…

A: (a) Maximize?(?1,?2,...,??)=?1?2...??n subject tog(x1,x2,...,xn)=x1+x2+.........+xn=cand xi>0By…