MATH 2321 Lecture Notes - Lecture 17: Directional Derivative, Unit Vector
13 Feb 2019
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Toflip) i z) du ip) = 5f (p): u=/f ip)| caso = - |ef(p)t. when cas 8=-17 0=50 = 180 in cosit=-1. Given f(x, y) = xe9 +x +sing, nd the directional denvative of f at point (1,0) in the direction of the vector (1,3). i sol. let n= (1,3), so d= x = (1/3) = (0, 2). Du f(p) = du (1,0) = 54(1. 0). in. 1/28/19 des suppose that f: r^ ir is differentiable at point ip. and m is a unit vector. Then the directional derivative of f at point ip in the direction of u is. || ef(p)/caso | where a - angle betw. @=(1,0) j y slope of the tangent like to the trace. Let u = 1, = (1,0) and p = (a,b). Du f (p)= ff (a,b)-(1,0) = (fx (9,6); fy(a,b)). (1,0). :) du p) attains the maximum value at point ip in direction of u= 5f (!p) and its max value is ff(p)).
