Find the directional derivative of f(x,y)=sin(x+2y) at the point (1, 2) in the direction pi/6.The gradient of f is:

Question

Find the directional derivative of f(x,y)=sin(x+2y) at the point (1, 2) in the direction pi/6.The gradient of f  is:

Answer 1

gradf(x,y) = <cos(x + 2y), 2cos(x + 2y)>.

gradf(1,2) = <cos5, 2cos5>

D_uf(1,2) = <cos5, 2cos5>•<cosπ/6, sinπ/6> = cos5cosπ/6 + 2cos5sinπ/6 = cos5(√3/2 + 1) = 0.52932