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 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_forward021 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_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
- 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_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_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_forward
- Find the directional derivative of the function at the given point in the direction of the vector v.. f(x,v) = e3xV – y?, (0,- 1), v= (2,3) -5 а. V5 7 b. V5 -7 C. d. -7 e V3arrow_forwardFind the directional derivative of f at P in the direction of a vector making the counterclockwise angle with the positive x-axis. 7 f(x, y) = 5√xy; P(1,4); 0= 3 NOTE: Enter the exact answer. Duf 1arrow_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
- 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_forwardDerivative of vector functions Compute the derivative of the followingfunctions.a. r(t) = ⟨t3, 3t2, t3/6⟩ b. r(t) = e-t i + 10√t j + 2 cos 3t karrow_forwardFind the directional derivative of the function at the point in the direction of the unit vector. 3 f (x,y)=sin(x+ 2y), P(2,– 1), u= 5 5arrow_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,