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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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Chapter 12 Solutions
Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
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- 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_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. 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.) Duf(-1,2) = -22 Incorrectarrow_forwardFind 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_forward
- Find the directional derivative of the function - 21 fax,y) = xe direction of the vector . a. O b = = = = 2 C₂ - VID По 2 d -4 at the point (1,0) in the deiarrow_forwardCompute the directional derivative in the direction of v at the given point. f(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) = 22 Incorrectarrow_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_forward
- Determine if the derivative of the vector-valued function exists at the specified point. (Your instructors prefer angle bracket notation for vectors. If the derivative exists at the specified point, enter its value. If the derivative does not exist, enter DNE.) FC) = (coste), tan(t), 3t cos(t) at t, =arrow_forwardGradient. Directional Derivative Find the directional derivative of f(x, y, z) = 2x2 + 3y2 + z2 at the point P: (2, 1, 3) in the direction of the vector a =i-2k. %3D %3D ion: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
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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