x x² + y² +z²' Hence, find its potential function. Given that F= y x² + y² +3²+y²+z²k ; prove that F is irrotational.

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: (B) If f(x,t) = fakt e-y²dy, then prove that kfx = ft.

A: (.)  Leibniz rule :  Given

Q: Find dy/dx by implicit differentiation. 6) x3 + 3x2y + y3 = 8 dy A) dx x2 + 3xy B) dy dx x2 + 3xy x2…

A:

Q: 2. Determine the directional derivative of o(x, y, z) = re" + y² + xyz at the point (2, 0, 3) in the…

A:

Q: 10. Find the derivative of y = V3x + 2. c) d) 3x a) 2V3x+2

A: Using derivatives

Q: Let f(x, y) = x/y. Then the directional derivative of f in the direction of √2 point (1, 1) is ○ (1,…

A:

Q: Find the first order partial derivative with respect to y of the function f (x, y) = x³y² + 3æe".…

A: Differentiate given function with respect to y treat x as a constant.

Q: Let f(x, y) = (x° + ay´, xʻy°, 2x+by), g(u,v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: f(x,y)=(x3+ay2,x2y3,2x+by)g(u,v,w)=(3u2+bv2+w3,uvw)To Find: Derivative of f(g(u,v,w)) using the…

Q: L(x) = b) Use the linearization to approximate 125.1 ~

A:

Q: The gradient of f(x, y) = xy at (x, y) = ( – 3, – 2) is %3D

A:

Q: Find the local linear approximation to f(x, y) = 4x² + y² at P(2,3)

A: We have to find the linear approximation of above function at (2,3) please see the explanation…

Q: n-manifold (n= 0, 1) '' , give an example whose topic is explained in detai

A: A topological manifold of dimension n or a topological n-manifold if it has the following examples:

Q: f(x, y, z) = x + tan(yz) exyz + 1

A:

Q: find the higher partial derivative of the following

A: Solve the following

Q: Q: Solve on white page clean and stepwise: Let f(x, y, z) = sinxyz, g(x, y, z) = x²yz, U = x²yi –…

A:

Q: Compute the partial derivative fa(, 4, 2) of the function f(2,4, 2) = yz' + 2 – 2 vy + * +2 y. O…

A:

Q: Let u(t)=6t3i+t2−4j−5k and v(t)=eti+9e−tj−e9tk. Compute the derivative of the following function.…

A: solve the following

Q: Provide the General Solution of each differential equations. Box your

A: Introduction: The equation dydx=f (x,y) of two variables x and y with its function f(x,y) defined on…

Q: Consider f(x, y) = xy(²-x²) x² + y² 0 if (x, y) = (0,0) if (x, y) = (0,0) . Show that fay(0,0) = 1…

A:

Q: Find whether the function F= 5yz? i+(3x– 2)}+(x² – xyJk is solenoidal.

A:

Q: Calculate Vf when f 3x 2- y z' + 4x'y + 2x - 3y - 5 at the point (1, 1, 0).

A:

Q: Consider the function f(x,y)=4x°y+2x?-y? +3y-5. Calculate the partial derivative f,(1,2). Answer:

A: