Computing directional derivatives with the gradient Compute the directional derivative of the following functions at the given point P in the direction of the given
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- Find the directional derivative of the function at the point P in the direction of the unit vector u = cos ôi + sin 0j. Sketch each the graph of the function, the point P, and the unit vector u. 1. f(x,y) = x² + y², P(1, - 2), 0 = .arrow_forwardFind the directional derivative of the function at the point Pin the direction the unit vector u = cos ôi + sin 0j. Sketch each the graph of the function, t point P, and the unit vector u. 2. f(x,y) = sin(2x + y), P(0, n), 0 = -.arrow_forwardCompute the directional derivative in the direction of v at the given point. S(x, y) = xy – x, v=i-j, P= (-1,2) Remember to use a unit vector in your directional derivative computation. (Give an exact answer. Use symbolic notation and fractions where needed.) Duf(-1,2) = -22 Incorrectarrow_forward
- Find the directional derivative of the function at the point Pin the direction of the unit vector u = cos ei + sin 0j. Sketch each the graph of the function, the point P, and the unit vector u. 3. f(x, y) = 3x – 4xy + 9y, P(1, 2), v = i +j.arrow_forwardFind the directional derivative of the function at the given point in the direction of the vector v. fx, y, z) = V xyz, (2, 2, 9), v = (-1, -2, 2) Pu(2, 2, 9) = Need Help? Read Itarrow_forwardCompute the directional derivative in the direction of v at the given point. f(x, y) = e*y-y, v = (12, –5), P = (-1,–1) Remember to use a unit vector in your directional derivative computation. (Give an exact answer. Use symbolic notation and fractions where needed.) Duf(-1, –1) =arrow_forward
- Compute the directional derivative in the direction of v at the given point. S(x. y) = xy - x, v=i-j, P= (-1,2) Remember to use a unit vector in your directional derivative computation. (Give an exact answer. Use symbolic notation and fractions where needed.) Du f(-1,2) =arrow_forward= Calculate the directional derivative of g(x, y, z) z² - xy + 3y² in the direction v = (1, -6,4) at the point P = (2, 1, −3). Remember to use a unit vector in directional derivative computation. (Use symbolic notation and fractions where needed.) Dvg(2, 1, -3) =arrow_forwardFind the directional derivative of the function at P in the direction of v. fx, y) 3 х3 - уз, Р(6, 3), v 3D (i + j) еВook Submit Answerarrow_forward
- 021 Bahar Which of the following is the directional derivative of f(x, y) =z²y at the point (-1,-1) in the direction of the vector i + 2j? O a. 0 O b. T V5 C. O d. Oe. hurava vaTınarrow_forwardUse the contour diagram of f to decide if the specified directional derivative is positive, negative, or approximately zero. ? ✓1. At the point (1, 0) in the direction of -3. ✓ 2. At the point (0, -2) in the direction of (2-23)/√5, ✓3. At the point (0, 2) in the direction of 3, 4. At the point (-1, 1) in the direction of (-7+3)/√2, ? ? ? ? ? V 5. At the point (-1, 1) in the direction of (-7-3)/√2, ✓6. At the point (-2, 2) In the direction of 7, V > 2.4 1.6 0.8 0 0.8 -1.6- -2.4 12.0 12,0 10.0 10.0 -2.4 6.0 -1.6 -0.8 0 X 0.8 4.0 (Click graph to enlarge) 1.6 12.0 10.0 8.0 10.0 12.0 2.4arrow_forwardFind the directional derivative of f at the given point in the direction indicated by the f(x, y) = 2ye-X, (0,4), 0 = 2π/3 Duf(0, 4) = 2 + √3 2 Need Help? Watch It Submit Answerarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage