Find the directional derivative of f(x,y)=sin(x+2y) at the point (-3, 1) in the direction θ=5π/6.c

Answer 1

f_x = cos(x + 2y), at (-3,1) f_x = cos(- 1) = cos1; f_y = 2cos(x + 2y); at (- 3, 1) f_y = 2cos(- 1) = 2cos1;

Unit vector in direction 5π/6 u = cos5π/6i + sin5π/6j

At (-3,1) grad f(x, y) = cos1i + 2cos1j

Direcional derivative: Df(x, y) = cos1cos5π/6 + 2cos1sin5π/6 = cos1(- √3/2 + 1)