Homework SourseFind the directional derivative of fxy sinx2y at the point
Find the directional derivative of f(x,y) = sin(x+2y) at the point (2,3) in the direction theta =5pi/6
the gradient of f is
gradient f = (....,....)
gradient f(2,3) =
the directional derivative is =
the gradient of f is
gradient f = (....,....)
gradient f(2,3) =
the directional derivative is =
Solution
grad f=(cos(x+2y),2cos(x+2y))
At (2,3)
grad f(2,3)=(cos(8), 2 cos(8))
In the direction 5/6=-/6,we are in the second quadrant
we have cos (5/6)=-1/2 and sin(5/5)=3/2
So the unit vector for direction is (-1/2,3/2)
Then the directional derivative is
(-1/2,3/2)*(cos(8),2cos(8))=-cos(8)/2+3cos(8)=-cos(8)(1/2-3)
