Show that the operation of taking the gradient of a function has the given property. Assume that u and v are differentiable functions of x and y and that a, b are constants.
(a)
(b)
(c)
(d)
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Calculus (MindTap Course List)
- obtain the gradient of the function f(x,y,z)=x^2y+5xzarrow_forwardFind the gradient of the function f(x, y, z) = √(x2 + y2 + z2), and the maximum value of the directional derivative at the point (1, 4, 2).arrow_forwardSuppose f(x,y)=xyf(x,y)=xy, P=(1,3)P=(1,3) and v=4i−3jv=4i−3j. A. Find the gradient of f.∇f=∇f= i+jNote: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P.(∇f)(P)=(∇f)(P)= i+jNote: Your answers should be numbers C. Find the directional derivative of f at P in the direction of vv.Duf=Note: Your answer should be a number D. Find the maximum rate of change of f at P.Note: Your answer should be a number E. Find the (unit) direction vector in which the maximum rate of change occurs at P.u=i+ jarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage