b. Find the directional derivative of the function z = x3 – y3 at the point M(1,1), in the direction of the vector u which makes angle a = 60° with positive direction of the x- axis.

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

A: Given function is, f(x,y)=sin(2x+y) and u=cos(-5π6)i+sin(-5π6)j⇒u=cos(5π6)i-sin(5π6)j=-32i-12j Now,…

Q: 4. For the function f(x,y) = 2x² – 3xy + 8y? + 2x – 4y + 4, find a tangent vector to the level curve…

A:

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: The three components of the derivative of the vector-valued function u are positive at t = t0.…

A: Given: The three components of the derivative of the vector-valued function u are positive at t =…

Q: Find the derivative of the vector function r(t)=ta×(b+tc), where a=⟨3,−2,−3⟩, b=⟨1,3,−2⟩, and…

A: To find the derivative of the vector function, rt=ta×b+tcWhere, a=3, -2, -3, b=1, 3, -2, and, c=-2,…

Q: Compute the directional derivative of the function g(x,y) = sin (x(4x – 5y)) at the point P(3, – 3)…

A:

Q: Find the directional derivative of the function f (x, y) = 7x² – 2.xy at the point P,(-3,5) in the…

A:

Q: Find the directional derivative of the function at the given point in the direction of the vector…

A:

Q: Find the directional derivative of the function f (x, Y, z) = 6x² –- 2xy + yz in the direction of…

A:

Q: In what direction ữ is f(x, y, z) increasing most rapidly at the point (1, 1, 0)? Give your answer…

A:

Q: Find the directional derivative of the function at P in the direction of v g(x, y) = /x² + y², P(3,…

A: Follow next step

Q: Calculate the directional derivative of f(x, y) = y – 2xy? at the point (0, 1) in the direction v =…

A: Solution

Q: Find the derivative, r'(t), of the vector function. r(t) = ( tan(2t), sec(5t),

A: We have to find the derivative of the given vector function  r(t)=< tan(2t) ,sec(5t) , 1/t^3>…

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: The function is given as f(x,y)=5xy . The point is x=2 and y=8 inclined at angle θ=π3. The…

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Givenf(x,y)=xx2+y2 , (2,1) , v=<3,5>

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A:

Q: Find the directional derivative, Dvf , of (*) f(x, y, z) = 4x tan 1 at the point P = (1, 1, 1) in…

A: To find the directional derivative of f(x,y,z) at P=(1,1,1) and the Direction, v=(1,2,2).

Q: Find the directional derivative of the function z(x, y) = In(x² + y²) at the point M(xo, Yo), in the…

A: The directional derivative of function z=fx,y in the direction vector u is calculated by the formula…

Q: Determine the directional derivative of the following functions in the vector direction specified at…

A: Here we will find out the required value.

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: Find the directional derivative of f(x,y) = x²y at the point P(-5,5) in the direction of v = 3i –…

A:

Q: Find the directional derivative of f(x,y) = x² + y² – 2x – 4y at the point (-2,3) in the direction…

A:

Q: Let f (x, y) = x² + 4xy². Say the directional derivative Du(1,1) with u is the unit vector that…

A:

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Please refer the attached image for complete solution.

Q: c) Find the directional derivative of f(x,y) = 10 – 3x2 + at P(2,–3) in the direction of the vector…

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 at the given point in the direction of the vector v.…

A: In this first we calculate derivative of g function then get a unit vector in the direction of v. So…

Q: find the directional derivative of the function in the direction of the vector u = cos i + sin j

A: Consider the given function, fx,y=sin2x+y Here we need to find the directional derivative of the…

Q: Find the directional derivative of the function f(x, y) = 2x2y + 6xy at (1, 1) in the direction of a…

A:

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Here we use the formula, Dvf(x,y)=∇f(x,y).v

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 f(x, y) = 10 − 3x^2 + (y^4)/4 at P(2, −3) in the direction of the…

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 directional derivative Du f(-3/8,1) for the function f(x, y) = cos(T(4x + 2y)) in the…

A:

Q: Find the directional derivative of the given function at the point P in the direction of vector u .…

A:

Q: h (r, s, t) = ln (3r + 6s + 9t), (1, 1, 1), v = 4i+ 12j + 6k

A: We have hr,s,t=ln3r+6s+9t at 1,1,1 in the direction of v=4i+12j+6k

Q: Find the Directional Derivatives of f (x, y) = ey at (2, 3) in the direction v = 3i – 4j

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A:

Q: Find the directional derivative of o = x2 + 2xyz – yz? at the point (1, 1, 2) in the direction of…

A:

Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = Vx2 + y2, P(3,…

A:

Q: Find the derivative of the vector function r(t) = (tan t, sec t,). %3D t2

A:

Q: 12. What is the directional derivative of f(r, y, z) = ba?y2² +x² + y? +22 in the direction of (8,…

A: Given that fx,y,z=bx2y2z2+x2+y2+z2 in the direction (8,9,12) find out the directional derivative

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

A:

Q: The directional derivative of xy f(x, y) = V2 (x + y) at (1, 1) in the direction of the unit vector…

A: We have ,  f(x , y) = xy2x + y   We know that , directional derivative at any point x , y is defined…

Q: Consider the following function: f(x, y) = xy? a) Find the directional derivative of this function…

A: The given function is- fx,y=xy2 Directional derivate of the given function at the point P( 1,1) is-…

Q: (b) Find the directional derivative of the function f(x,y,z) = xy sin z at the point (1,2, %3D T2)…

A: Solution:

Q: If asked to find the directional derivative of f(r, y) in the direction of a NON unit vector (a…

A:

Q: The directional derivative of f(x, y, z) = x? + y? + 4xz at Po(1,-2,2) in the direction of the…

A:

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

A: