Let a function f(x, y, z) be such that Vf(P)=[2,4, 3]. The value of directional derivative D,f(P) where u= - [-1, 1,-1] is given by O A V3 OB. 1 OC. 7 O D. None of these

Q: Assuming that the necessary derivatives of f(x, y, z) are defined, how are Dˆi f, Dˆj f, and Dkˆf…

A: .

Q: Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), e" + cos(v)). Use…

A: Using total derivatives:

Q: Find the directional derivative of the function at P in the direction of v f(x,y,z xy + yz + xz,…

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: Let f (x, y) = xe^y , P = (2, −2), and v =〈3, 4〉. Calculate the directional derivative in the…

A: Given function is  f(x, y)=xey Point P=2, -2 and direction v=3, 4.

Q: The maximum directional derivative of the function f (x, y, z) = x'y°z° at the point (1, 1, 2) is a)…

A: Given problem:- Find the maximum directional derivative of the function f(x, y, z) = x³y³z³ at the…

Q: Let f(x, y) be a function such that F(s,t) = f(s – 2t, ť²) fr(2, 1) = 5, fz(0, 1) = 3 fy(2, 1) = –1,…

A:

Q: Let f(x, y) = xeY, P = (2, -1), and v = (2, 3). Calculate the directional derivative in the…

A: The given function be: Now,

Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

A:

Q: Find the derivative of f(z)= In(z-+-3z+2i). O (A) ƒ'(2) = O (B) ƒ'(2) = O (C) ƒ'(2) =1 – O (D) f'(z)…

A:

Q: a) Find directional derivative of the function at P, in the direction of u where f (x, y, z) = x? yz…

A: From the given problem:   fx,y,z=x2yz+4xz2, P01,-2,-1u=2i+j-2k   From the expression of the…

Q: { z sin a). if (x, y) # (0,0) 2. Determine if a function f: R2 R defined by (. 9) = BE 0, if (KJ) =…

A:

Q: 1) Find the directional derivatives as a shown function of f at P (1,2,3) in the direction from P to…

A: Consider the function f(x,y,z)=x3y-yz2+z. P=(1,2,3) and Q=(4,5,2). Directional derivative of…

Q: Find the directional derivative of the function at P in the direction of v. 1 = √₂ (i+j) f(x, y) =…

A:

Q: Find the directional derivative of f at P in the direction of a. f(x, y, z) = xy + z²; P(5,–1,–1);…

A: Determine the gradient of f. ∇fx,y,z=∂f∂x+∂f∂y+∂f∂z=∂xy+z2∂x+∂xy+z2∂y+∂xy+z2∂z=x+y+2z Now determine…

Q: Determine the value of m such that the function *- y - 2 E + 2 vỹ VI – Vy ; z +y f(x, y) = is…

A:

Q: Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), eu + cos(v)). Use…

A:

Q: g(x, y, z) = xye, P(2,4, 0), Q0, 0, 0)

A: The given function is  g(x, y, z) = xyez

Q: Find the directional derivative of f at P in the direction of a. f(x, y, z) = xy + z²; P(-5,–5,4);…

A: Here we have to find the directional derivative of f(x,y,z)=xy+z2 at P(-5, -5, 4) in the direction…

Q: Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), e“ + cos(v)). Use…

A:

Q: 2B. Find the analytic function f(z) = u+iv for which v= e(xcos y+ ysin y)

A:

Q: Let u(t) = (3,3tt) and v(t) = (3r, - 21,2). Compute the derivative of the following function. %3D…

A:

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

A:

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

A:

Q: Let f(x, y) be a function such that F(s, t) = f(s – 2t, t²) fz(2, 1) = 5, fz(0, 1) = 3 fy(2, 1) =…

A: Explanation of the answer is as follows

Q: Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), eº + cos(v)). Use…

A: Given: f is a differential function of x and y . gu,v=feu+sinv,eu+cosv         Objective is to…

Q: A. Verify Clairaut's Theorem for the given function: F(U,W) = Sin(UW)- 4U?w2 %3!

A:

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A: Given the function f(x,y)=ycos(xy). We need to find the directional derivative of f at the point…

Q: Find the directional derivative of the function at the given point in the directic h(r, s, t) =…

A:

Q: Let f (x, y, z) = xz cos(y). Find the directional derivative of f at (1,0, 2) in the direction of v…

A:

Q: Let a function f(x, y, z) be such that Vf(P)-[4, 3, 2] The value of directional derivative D,f(P)…

A:

Q: Let f(x, y, z) = y*x cos(27) + tan-(4z). Then find the directional derivative of f at the point Po…

A:

Q: Sketch E and then evaluate // f(r, y, 2) dV for the specified function. (a) f(x, y, z) = =;…

A: Hey, since there are multiple subparts posted, we will answer the first question. If you want any…

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 – y3, P(6,…

A: Solution is given below:

Q: compute the directional derivative of f in the following case: 12. 3 4 f(r, y, z) = x"², x= (e,…

A: We will find out the required value.

Q: Find the directional derivative of the function at P in the direction of Q. g(x, y, z) = xye⁹², P(2,…

A: Given :gx,y,z=xye9zP2,2,0, Q0,0,0

Q: Suppose u and v are differentiable functions of x. Use the given values of the functions and their…

A:

Q: Let f(x, y) = x² + y? and C be the curve along y = x² from (0, 0) to (1, 1).

A:

Q: Find the directional derivative g(x, y) = x² + y², of the function at P in the direction of v. P(5,…

A:

Q: Find the directional derivative of the function at P in the direction of v. f(x,y,z) = x²+y²+z²…

A:

Q: Using the definition, find the Directional derivative of function f(x, y, z) = x? + 2y? – 3z? at…

A:

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A:

Q: Let f(, y) = In(?y+ 2 ). Find the directional derivative of f at the point (1,1) in the direction of…

A: Directional derivatives along vector u is <fx,fy><u>

Q: 2. Find the maximum value of the directional derivative, D f, of the function _2 f(x, y, z) = x´ +…

A:

Q: Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), eu + cos(v)). Use…

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: Exercise 3: Find A and B given that the derivative f'(r) is everywhere continuous, and Aa2 Bx 2, x<2…

A: The function f(x) whose derivative is everywhere continuous is given by,

Q: Let f(x, y, z) = 5x – y + z?. Find the maximum value M for the directional derivative at the point…

A:

Q: In Exercise find the directional derivative of f at the point P in the indicated direction. f(x, y)…

A: Since you have asked more than 3 questions, I am solving first 3 questions. Please repost the other…