1. Determine the nature of the stable points of the function f (x, y) = x²y – x² – 3xy + 3x + 2y – 2.

Q: Find all second order partial derivatives of the functions given below. (a) f(x, y) = xy² + x²y³ +…

A:

Q: Find the first partial derivatives of the function. w = In(x + 4y + 8z) Əw ax aw ду aw II II II

A: Given, w= ln(x+4y+8z)

Q: Find the first partial derivatives of the function (2x + 9y)'². = Z dz 1. дх dz 2. ду

A: To find the first partial derivatives of the function: z=(2x+9y)12 So, z is the function of x and y.

Q: Find the first partial derivatives of the function

A: NOTE : As you have uploaded multiple questions without specifying which one to solve, we will answer…

Q: Find the first partial derivatives of the function. f(x, t) = Vx In(t) 1 cln(t) 2Vx fx(X, t) fe(x,…

A:

Q: 5.6 8.7 Find the four second-order partial derivatives for f(x, y) = 7x°y° + 3x°y".

A: To find the second order partial derivatives

Q: 1) Find the first order partial derivatives of the functions. a) f(x, y) =x* – 2x²y³ b) g(x, y) =…

A:

Q: 10. Find the first and second order partial derivatives. (10a) f(x,y) = 4x² + y³ – 3xy (10c) f(x, y)…

A: In partial differential of function with respect to x we assume other variable (y)  as constant and…

Q: Find the first partial derivatives of the function. z = (4x + 6y)5 az (No Response) ax az (No…

A:

Q: Find the first partial derivatives of the following functions: 5. y = Vx? – y2 6. z = In(x + /x? –…

A:

Q: a) z=x² In (x y²) b) z=4 cos(x-3y)

A: As we know that; The Power law: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g' The Chain rule:…

Q: Find the following higher order partial derivatives. x3+y2+z2=5 (A)   ∂2z/∂x∂y= (B)   ∂2z/∂x2=…

A: Given that      x3+y2+z2=5→           i       differentiatting partially w.r.t 'x' we get…

Q: f(x, y) = xVy + y²; (2, 1)

A: The function is fx,y=xy+y2.   Determine the partial derivative with respect to x.…

Q: 2. Calculate the partial derivatives of each of the following functions: 2.a2y x² + y? (a) f(x, y)…

A:

Q: Find the first order partial derivatives of the function, w=xz-5(x^2)(y^3)(z^4)+ln(x*y^2*z).

A: w(x,y,z)=xz-5x2y3z4+ln(xy2z)

Q: Find the first partial derivatives of the given functions. 1. z = x+y / x-y 2. z = ln (x2 + y2)

A:

Q: Find the first partial derivatives of the following function. f(x,y)=x²-3xy-6y²

A:

Q: Find the second order partial derivatives of the function: f(x,y)=x* +xy° +x+4.

A: In the case of function of two variables there will be a total of four possible second order…

Q: Find all the first and second order partial derivatives of z for the following function: z = x2 – xy…

A:

Q: 9. Find all second order partial derivatives of the functions given below. (a) f(x,y) = x*y³ + x²y³…

A:

Q: Find the first partial derivatives of the function z = (2x + 3y)10.

A:

Q: 1 Compute all the partial derivatives of the following functions: 1.1 f(x, y) = "-4 a+y 1.2 f(x1,x2)…

A:

Q: Find the first partial derivatives of the function f(x, y, z) = xz – 5x²y³z*.

A: Find the first partial derivative of function f(x,y,z)

Q: 9. Find all second order partial derivatives of the functions given below. (a) f(x,y) = x*y³ + x²y³…

A:

Q: a) 4x²y - 3xy³ + 6x; d) e²x+3y; b) xy; e) x+y x-y c) xy²; f) 3x²y-7x√y.

A:

Q: 16. f(x, y) = x+y³ + 8x²y

A:

Q: Find all second order partial derivatives of the given functions f(x, y) = cos(2xy2 3x?y3)

A: Consider: fx,y=cos2xy2-3x2y3. Calculate: ∂2f∂x2. Apply chain rule: ∂u∂x=∂u∂v∂v∂x Let u=cos2xy2-3x2y3…

Q: Please solve. the symbol is partial is derivative

A:

Q: A. Find the first partial derivatives of the given functions. 1. z = x3 – xy? + 3y²

A: For a function in several variables partial derivatives are derivative with respect to one variable…

Q: (4) Let f(x, y) = xy² +2. Find all first-order and second-order partial derivatives.

A:

Q: a) f(x, y) = (4x²y4 – 3x² + 8y³)³ x + y c) g(x, y) = In sen b) f(x,y) = x ln y + y ln x

A:

Q: Find the first partial derivatives of the function. f(x, y) = x/ 1 + yo 1+y5 2 5 x 1+ y 4 5xy1 *…

A: We have to find derivative

Q: Find all second-order partial derivatives of the function. f (x,y) =x³+xy³ + y²

A:

Q: Please solve for  d^2f/dx^2=d^2f/dydx=d^2f/dy^2=d^2f/dxdy=

A:

Q: Q1: Find all the second order partial derivatives of the functions: x-y (1) f(x, y) = x2+y (2)…

A:

Q: and the first partial derivatives of the function. f(x, y) = 4y

A: Given the query is to find indicated partial derivative.

Q: 1)Calculate the partial derivatives of first-order of the function f(x.y) =³.cos(xy) + e"x°y°

A:

Q: find all the second-order partial derivatives of the given function f(x,y)=xy^(2)+ye^(xz)+5

A: It is partial derivative

Q: 2. Calculate the partial derivatives of each of the following functions: 2x²y x² + y? (a) f(x,y) (b)…

A:

Q: Q2: (a) Use implicit differentiation to find out the partial derivatives ay/Əx1 and ay/ax2. F(x1,…

A: Function is the unique relation where each x is mapped to a unique y. It can be of many types:…

Q: Q1: Find partial derivatives of the function with respect with each variable 1) f(x, y)= 2x² – 3y –…

A:

Q: Find the first partial derivatives of the function. f(x, y) = x5y %3D Fx(X, y) = | 5yx5v–-1 fy(x, y)…

A:

Q: dz 1. dz ду || 2.

A: The given function is: z=(2x+7y)12.

Q: Find all second partial derivatives of the function f(x, y) = (x + 1)³ + 2xy + y³

A: take the partial derivative with respect to x

Q: Find the Partial Derivatives of t 1) f(x,y) = 2x - 3y -4 2) S(x, y) = (x' -1Xy+ 2) 3) f(x, y) =…

A:

Q: Find the first partial derivatives of the function. f(x, y) = x^y³ + 8x5y 4,3 %3D

A:

Q: Find the first partial derivatives of the given functions. 1. z = x3 – xy? +3y² 2. z = 3x?y - y3 +…

A:

Q: Find the partial derivatives: fx, fy, and f₂: f(x, y) = x5y³ ln(x³ + y²) b. f(x, y, z) = x²y -…

A:

Q: Find all the second partial derivatives of the function f(x, y) = 8xy^2+xtany

A:

Q: #3. Find all the 2nd order partial derivatives for the given function h(x,y)=x*y2 - 4xy+e7y + In…

A: