8. Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0, –3,5)

Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

Q: EX Prove that the directional derivative of f(x, y) = y² + 2xy³ + x²y² at point (0, 1) in the…

A: What is Directional Derivative: The directional derivative of a scalar function represents the rate…

Q: Q2: a) If W =F(x,y), where x =v -g and y = 2vg calculate W +W, b) What is the directional derivative…

A: Given that w = Fx,y  , where x = v2 = g2 and y = 2vgWe have to calculate wx2 + wy2Now, we know that…

Q: Find the linearization of the function f(x,y) = ln(x3y6) at the point (x0,y0) = (4, 3). Leave all…

A: Given fx,y=lnx3y6     at (4, 3) The linear approximation in 2 variables is given by Lx, y=fa,…

Q: 3. Prove that the directional derivative of f(x, y) = y² + 2xy³ + x²y² at point (0, 1) in the…

A:

Q: If f(x, y, z) 2x5 + 3y5 - 8x2y2z2, what is the partial derivative of f with respect to z?

A: The given function is fx, y, z=2x5+3y5-8x2y2z2.

Q: Find the value of dz at the point (1)1, If the equation 5xy+ z4x -Qy2 =4 %3| defines z as a function…

A: Given 5xy+z4x-2yz=4to determine dzdx  at  (1, 1, 1)

Q: 12. Let f(x, y, z) = xy – 2³. Calculate the directional derivative of f at the point (3, -2, –1) in…

A: We have to find direction derivative

Q: Find the diectional derivative of the function f (xiy,z)= sin (xy+2) at the point of P(1, al2 x4) a…

A:

Q: 8. Find the directional derivative off at the p in the direction of v = () of f(x, y, z)=x²exx, p =…

A:

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P. (0,0,0) in the…

A: We have a given function g=3e^x cos(yz)

Q: 2. Find a function f(x, y) which is NOT linear in either a or y and for which the tangent plane at…

A:

Q: Q4:- Find the derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² +…

A:

Q: 12. Find the directional derivative of f(x, y, z)=zy+yz+xzat (1, 1, 2) in the direction of u =…

A: We can find the directional derivative in the following steps.

Q: Solve for the partial derivative with respect to x, y and z f(x, y, z) = x²y + xy² + 2xyz

A:

Q: 5. Find the gradient of cos(xy) – 3y* + 3 at the point (1,4)

A:

Q: b) Find the directional derivative (D.) of the function at P in the direction of PQ f(z, y) = sin 2z…

A:

Q: 32 Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional (1, 2) and…

A: Given problem:- Suppose that f(x, y) = x3 y2 . The directional derivative of f(x, y) in the…

Q: Q2 / Find the directional derivative of f(x.y.z) 4xy +5xz2 +6yz2 At the point P(3,1,4) in the…

A: ∂f∂x=4y+5z2∂f∂x=84∂f∂y=4x+6z2∂f∂y=108∂f∂z=10xz+12yz∂f∂z=168Therefore, the gradient is∇f (3, 1, 4)…

Q: 8. Find the directional derivative of f (x, y, z) = xyz3 at P(2, 1, 1) in the direction of Q(0,…

A: Ans=1 I have considered image question bcz I think you have done mistake while typing... Now go…

Q: Find the derivative of the function at Po in the direction of u. f(x, y, z) = In(x 2 + 3y 2 + 9z 2),…

A: Given that      f(x,y,z)=ln(x2+3y2+9z2), P0(3,3,3), u=3i+4j Here we have to find the derivative of…

Q: Find the maximal directional derivative magnitude and direction for the function…

A: Consider the given function and point, f(x,y)=x3+2xy-cos(πy),(3,0) Now, find the derivative with…

Q: Find the gradient of cos(xy) – 3y4 + 3 at the point (1,4) -

A:

Q: Consider the function g defined by 1 g(x, y) = cos (Tx /y) + log3 (r y) In what direction does g…

A:

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz (B)If Z =…

A:

Q: Find the derivative of f (x y z) = x^3 − xy^2 − z at (1, 1, 0) P0 in the direction of A = 2i - 3j +…

A: Given,           f(xyz)=x3−xy2−z  and point Po =(1,1,0) and the direction vector A=2i-3j+6k.

Q: 1. Find the directional derivative of the scalar function f = yzx^2 + 4xz^2 at the point P(1,-2,-1)…

A:

Q: Q1: Find the derivative of f(x,y,z)=x^3-xy^2-2z at point P_o (1,1,0) in the direction of vector V…

A: Q1:   Given: f(x,y,z)=x3-xy2-2z with the point P0 (1,1,0)v=2i-3j-6kTo find:The directional…

Q: Find the directional derivative of F(x , y , z)=7y2e−x+3z2 in the direction u=(3,6,−2) at the point…

A: We have to solve

Q: B. Use the definition of directional derivative to solve Duf(x0, Yo, zo) at point P(xo, Yo%o) where…

A:

Q: 2. Find the derivative of f(x, y, z) = x³ - xy2 - z at Po(1,1,0) in the direction of V = 2ỉ – 3j +…

A:

Q: Q1: Find the derivative of f(x,y,z)=x^3-xy^2-2z at point P_o (1,1,0) in the direction of vector…

A: Solution:-

Q: a) If W = F(x ,y),where x =v²-g and y 2vg calculate W +W, %3D b) What is the directional derivative…

A: W=f(x,y) and x= v2-g2 & y=2vg   Wx = dW/dx = (df/dx*dx/dv) + (df/dx*dx/dg) ..............From…

Q: 10. Let f(x, y) = x² + y³. Calculate the directional derivative of f in the direction of = (4, 3) at…

A: The given function is: f(x,y)=x2+y3Direction vector is:  v→=4, 3Given point:  P=(1, 2)

Q: 3x The directional derivative of f(x,y,z) = ln (주)을 1+yz from P to Q(-1,-1,2) is given by...…

A: We can solve this using given information

Q: Find the directional derivative of f(z, y) = In(e" - 3y) at the point (0,0) in the direction of 3i +…

A:

Q: 8y If the directional derivative of f(x,y)D at (2,1) in the direction of (a, 2) is equal to zero,…

A: Given,            f(x,y)=8yx

Q: If f(x, y, 2) = cos(x - y)+e² , compute directional derivative of f at (5, 5, 0) in the direction of…

A:

Q: 3. Evaluate the gradient of S(1, y, 2) = In(cosh z+ y) - arctan| at (1,y) = (7/2, 1).

A: Given that fx,y,z=lncosh x+y-z2 arctanx2y2+z2 To find the gradient of f(x,y,z) :…

Q: 1. Find the directional derivative of g(r, y, 2) = :2 - zy + 2y? at P = (2,1, -3) in the direction…

A:

Q: Q2: a) If W = F(x ,y), where x =v²-g and y = 2vg calculate W +W, b) What is the directional…

A:

Q: 2. Find the directional derivative of f(x, y, z) = y – Væ² + z² at P(-3,1,4) in the direction of a =…

A: Given f(x,y,z)=y-x2+z2

Q: 23. Find the directional derivative of f(x, y) = *+y at P(1,0) in the direction of Q(-1,-1).

A:

Q: 12 Use the gradient to find the directional derivative of the function at Pin the direction of Q.…

A:

Q: 1. Find the directional derivative of the function f (x, y, z) = In (3x + 6y + 9z) at the point…

A: To find: the directional derivative of the function f(x,y,z)=ln (3x+6y+9z) at P1(1,2,3) in the…

Q: Let f(x, y) = -4x + 3y. Find the directional derivative in the direction of v = from the point P =…

A:

Q: What is the directional derivative of f(x,y,z) = ln(x²+2y²+ 4z²) at the point P(-1, 2, 4) in the…

A: The given function is; f(x,y,z)=ln(x2+2y2+4z2) Point P(-1,2,4) u=-3i/13 -4j/13 -12k/13.

Q: (b) Show that the function defined by xy √√√²+y² f(x, y) 0 if (x, y) = (0,0) is not differentiable…

A: We have to show that the function defined by…

Q: . Find the directional derivative of the function f(x,y, z) = xy+yz + zx at M(2,1,3) in the…

A:

Q: Solve for the partial derivative with respect to x, y and z f(x,y,z) = x²y + xy² + 2xyz

A: