What is the directional derivative of the function f (x, y) = 2xy – 3y2 at point p.= (5,5) in the direction of u = 4i + 3j? %3D а) 3 b) - 2 c) 6 d) – 4 e) -3 f) 2 g) None of them

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: Match the D.E. with a direction field: y' = t+y – 1, , y' = sin(t)sin(y), , y' = 2 – y, , y' = t(2 –…

A: NOTE: Horizontal axis is t-axis  .

Q: Consider f(z, y) = Vzy+ 2y? ry- %3D Approximate f(2.4, 1.04) by using the tangent plane.

A: f(x,y)=xy+2y2

Q: Match the D.E. with a direction field: y' = t+ y – 1, , y' = sin(t)sin(y), , y' = 2 – y, , y' = t(2…

A: NOTE: The horizontal axis is t-axis.

Q: Verify that u is a solution to the equation ugx + Uyy + u zz = 0. u(x, y, z) = e4z+3y cos(5z)

A: Follow the procedure given below.

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

A:

Q: Evaluate | f(x,y) ds where Cis the portion of the curve y = In x from the point (1,0) to the point…

A:

Q: 3. For all a? + y + 2? > 0, verify that the velocity potential 1 $(r, y, z) = Vr? + y² + z2 is a…

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 multiple questions, we will solve the first question for you. If you want any…

Q: 1) For f(x, y,z) = x2 – (1 – y)? + z?. Find directional derivative of f at P(1, 1, 1) in the…

A: Given that  f(x,y,z)=x^2-(1-y)^2+z^2 Point P(1,1,1) Vector is a=(0,3,4)  To find the directional…

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

A:

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

A: As 2 questions are given, I will solve only one : We are given: f(x,y,z)=z2exy and the point is…

Q: 5. Show that the equation of the tangent plane to f(r, y, z) = c at (ro, yo, 20) is given by the…

A: Given: Surface f(x, y, z)=c and a point x0, y0, z0 To show: Equation of tangent line to f(x, y, z)=c…

Q: (r, y, z) = sin 2x i + xz cos y j+ e*y iv F,

A:

Q: Consider f(x, y) = x³y+ 2xy? Approximate f(2.1, 1.03) by using the tangent plane.

A: Given f(x, y) = x³y + 2xy² Find f(2.1, 1.03) using tangent plane.

Q: Compute the directional deri vative of the function f(z,y, 2) = zy² + y²9+°% at the point P(4, –2,…

A: Given function is fx,y,z=xy2+y2z3+z3x

Q: What is the directional derivative of the function f(x, y, z) = 2xy + z² at the point (1, –1,3) in…

A: The Directional Derivative: Let the function f(x, y) be the height of a mountain range at each point…

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: For f(x,y, z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: The directional derivative of a function f  in the direction of the vector u is given by…

Q: Consider z as a function of æ and y and z = Ax + By + D be the tangent plane to f(x, y) = 2a² + 2y³…

A:

Q: Suppose X and Y has a joint pdf given by f(x, y) = 6x, 0 < x < y < 1, and zero otherwise (a) Find…

A:

Q: In Exercise nnd the directional derivative ofJ at J at the point P in the indicated direction. f(x,…

A: The given question was taken from the vector calculus in which we have to find the directional…

Q: Consider the function 422 + Vy+3z . f(x, y, z) = 3x – 7 Find the directional derivative of f at the…

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 derivative of f(x, y) = x² + xy at P,(1,2) in the direction of the unit vector u = i+ V2

A:

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

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: Find the directional derivative of f(x, y, z) = x²y−yz³ + z at the point (1,−2, 0) in the direction…

A: Solution:f(x, y, z) = x²y−yz³ + zat the point (1,−2, 0) in the direction of the vector a = 2i +…

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: Let e =, f(x,y) = 3x°y-4xy°+ ay-4x at (3,4) in the dire ction given by the angle. Find the…

A: Solution is written in below steps.

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

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

A:

Q: The directional derivatives of fx, y,z) = xy+ 4y°z+ 3xz? at (3,3,3) in the direction of y = 31 + 6j…

A: The function is f(x,y,z)=x3y+4y2z+3xz2 at the point 3,3,3 in the direction of v→=3i→+6j→+6k→. Find…

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

A:

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

A:

Q: Consider z = Ax + By + D be the tangent plane to f(x, y) = 2x² + 5y³ + 9xy + 9x + 3y at (6,9).What…

A:

Q: 1. (a) Let /(r,y)- cos(z + 2y). Compte the directional derivative Da/(r.y), where u- (b) Compute ff,…

A: Given that, In part (a), f(x, y) = cos(x+2y) u=(x,y)=-12,12 We have to find the directional…

Q: Assuming that the equations define y as a differentiablefunction of x, use Theorem 8 to find the…

A: Given:           x3−2y2+xy=0,     (1,1)

Q: Compute the directional derivative of f at the given point in the direction of the indicated vector.…

A:

Q: 5. Show that the equation of the tangent plane to f(r, y, z) = c at (ro, Yo: 20) is given by the…

A: This is the question from vectors.

Q: Which of the following is the directional derivative of f(r, y) = z'y at the point (-1,-1) in the…

A: The directional derivative formula is given by Duf(x,y)=∇f(x,y)⋅u, where u is the unit vector and…

Q: (b) Evaluate (3, 10) J(0, 1) Cto (3x + y) dx +(2y - x) dy along- @ curve y= x? +1; (ü) the line…

A: Given function is 3x+ydx+2y-xdy i) Given curve is y=x2+1 Hence the integrand becomes…

Q: Assuming that the equations define y as a differentiablefunction of x, use Theorem 8 to find the…

A: Consider the given function, xy+y2-3x-3=0 now differentiate with respect to x,…

Q: Consider z = Ax + By + D be the tangent plane to f (x, y) = 5x² + 10y³ + 6xy + 8x + 7y at (-0, 4).…

A:

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 f(x, y) = x²y and ʊ = 47 – 37, find the directional dervative at the point P = (3, 6) in the…

A:

Q: For f(x,y,z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: Since there are two questions posted, we will answer the first question posted (1). If you want the…

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

A:

Q: find the general solution of the dipperential ation given below. y+ 2xy -xe-r?

A:

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

A:

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