Find the directional derivative of the function f(x,v) at point p in the direction of vector a. 1) fix, y) %3D 4x2 - хv + 5y2, р %3D (-3, -5), а %3Dі - 2; = XV A) 15/5 B) 3 515 C) 253 D) 13
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- 2. Find the directional derivative of 9 = yx? +x?z + 3xyz in the direction of vector n = Î + 2ŷ -? .Find the cartesian equation of the straight line tangent to the plane curve given by the vector equation r(t) = (t- 6) i + + 3t - 2) į. at the point P(-5,4) on the curve. Express your answer in the form y = ax + b , where a and b are integers. equarion of the tangent line is given by y = 9x + 49Calculate the directional derivative of g(x, y, z) = z² - xy + 4y² in the direction v = (1, -6,4) at the point P = (2, 1, −8). Remember to use a unit vector in directional derivative computation. (Use symbolic notation and fractions where needed.) Dvg(2, 1,-8)=
- Find the directional derivative of f(x,y) = x² + y² – 2x – 4y at the point (-2,3) in the direction of the vector w = 3i – 4j. 1. - 2. - 3. -4 4. – 5. -Evaluate the directional derivative Duf (2, 3) if ƒ (x,y) and T2 - y u is the unit vector in the same direction as (-3, 4).Given that the directional derivative of f at the point (8,-1,7) in the direction of a = 8i - 4jk is - 5 and that ||Vƒ(8,-1,7)|| = 5, find Vf(8,-1,7). Vƒ(8,-1,7) =
- 1) Find the directional derivative of f at the given point P in the direction of the point Q. f(.v)-Ary 12r- P- (3,0), Q-(1,0) f(r.g)%3D1ry1 2r P (3,6), Q-(4,9)Calculate Duf(− 4, − 4, 1) in the direction of f(x, y, z) − x² + 5xy + 5y² + 3x Round your answer to four decimal places. = = 27-37-k for the function 3yz + 4z²+xz.