2. Let T(x; y) = sin(2x – y) , P (-; ) and Q(0;0) (a) Determine the directional derivative of T at P in the direction from P to Q. (b) Determine a unit vector in the direction in which T increases most rapidly at P. (c) Find the unit vector in the direction in which T decreases most rapidly at P, and determine the rate of change of T in this direction.

Q: Compute the derivative of the vector-valued function r(t)=⟨sin2t,et2⟩.

A: In order to compute the derivative of the vector-valued function: Differentiate the vector function…

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: Find your answer below

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

A:

Q: Consider the function f(x, y) = y ln x - x ln y - . a Find the directional derivative of f at the…

A:

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 directional derivative of f(x, y) = cos(x) + y² at (T,2) in the direction of (3, –4).

A:

Q: Find the derivative of ƒ(x, y, z) = xyz in the direction of the velocity vector of the helix r(t) =…

A: Concept: A vector is a directed line segment whose length is the magnitude of the vector and with an…

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

A:

Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: Since, you have posted multiple question. I am answering first one. Please post again with specific…

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: 2. Find the rate of change of the function f(x, y) = x² sin y at the point (1,) in the direction of…

A: To find out the rate of change in the direction of the given vector.

Q: B. Find the directional derivative of the function f(x.y): X-y at the point (1.-1) Duts xy+1 in the…

A:

Q: A particle moves in a plane according to -t, x = (t+1)e; y=2tet -t Determine the simplified…

A:

Q: Let f(x, y, z) = 3ex cos(yz). a) Find the directional derivative of f at P(0, 0, 0) in the…

A: Given , fx,y,z=3ex cos4zwe have to find directional derivative of f at p 0,0,0 in the directionof…

Q: Find the derivative of the vector function 7(t) = (t sin t, t2, t cos 2t).

A:

Q: b. Find the directional derivative of the function z = x3 – y3 at the point M(1,1), in the direction…

A:

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: Given :fx,y=sin8x+yp0, π

Q: Find the directional derivative of the function f(x, Y, z) = x + ln(y² + z²) at the point A(2,1, 1)…

A: To find the directional derivative of the function f(x,y,z)=x+ln(y2+z2) at point A(2,1,1)  in the…

Q: Compute the directional derivative of f(r.y) = at the point (1, 1) in a direction normal to the…

A: Given that: f(x,y)=x2y at the point (1,1) Ellipse: x2+2y2=1 at the point (1,0)

Q: Consider h(x, y, z) = cos (xy) + eyz + ln (xz). Determine the directional derivative of h at the…

A:

Q: Find the derivative of f (x, y,z) = xyz in the direction of the velocity vector of the helix…

A: Answer and explanation is given below...

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A:

Q: Find the directional derivative of the function in the direction of the unit vector u = cos e i +…

A: This question is based on del operator.

Q: Suppose that the directional derivative of a function f at a point P in the direction of the vector…

A:

Q: Find the directional derivative of the function f(x, y,z) =x-y+2z at the point P(1,2,3) in the…

A: Note:- Let a function f(x, y, z), then Direction Derivative of the function f at point P in…

Q: Find the derivative of the function at Po in the direction of vector A h(x, y, z) = cos(xy) + e>% +…

A:

Q: 2 - What is the directional derivative of the function f(x,y,z) = x3 - 2xy +z at point Ao= (1,1,0)…

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: Find the gradient of the function w = 1/(√1 − x2 − y2 − z2),  and the maximum value of the…

A: The given vector is:

Q: Compute the directional derivative of f (x,y)= at the point (1,1) in a direction normal to the…

A: The directinal derivative is given below

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A:

Q: 4. Compute the directional derivative of f(r, y) = at the point (1, 1) in a direction normal to the…

A:

Q: Let f(x, y) = sin(x – y). Calculate the directional derivative of f in the direction of v = (1, 1)…

A:

Q: 3. Find the derivative of the function f(r, y, z) = In (z2 +y + 4z + 5) in the direction of the…

A:

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

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: - Consider the function g defined by 1 g(x, y) = sin 2 log3 (x – y) 1. Calculate the instantaneous…

A:

Q: Given function f(x, y) = xy² - x² + 5y. a) Find the maximum rate of change of f at the point (1, -2)…

A:

Q: 11. Calculate the directional derivative of the function f(, y, z) = xyz at the point a (-1,0,2) in…

A: See the answer below

Q: Find the directional derivative of f(x, y, z) = xy² + yz% at P(1, – 1, 1) in the direction of a = i…

A:

Q: 3. Let f(x, y) = In 2x + 4y, find the directional derivative of f(x, y) in the direction of at the…

A:

Q: Choose the direction vector for which the function f defined by f(x, y)= sin(5x) cos(3y) has the…

A:

Q: 2 - What is the directional derivative of the function f(x, y, z) = x° - 2xy + z point A, = (1,1,0)…

A:

Q: Consider the function f(x, y) = y ln x - x ln y - . a Find the directional derivative of f at the…

A:

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

A:

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A:

Q: What is the directional derivative of f(x, y) = 4xy+ y cos x at the point (0, 1) in the direction of…

A:

Q: 3. Find the directional derivative of the function f (x, y)= sin (xy) at a point -2i +j in the…

A: The given function: f(x, y)=sin2(xy)P=34, πu→=-2i^+j^5

Q: Find the directional derivative of the function f(x, y) = tan-(/xy) + li + 2j. Note that In(1 + xy)…

A: