Câu hỏi
Evaluate the directional derivative of the function f(x,y)=arcsin((x)/(y)) M(5,12) in the direction of the vector overrightarrow (u)=(1,1) Answer: square
Giải pháp
4.3
(186 Phiếu)
Ngọc Châu
thầy · Hướng dẫn 5 năm
Trả lời
The directional derivative of a function
at a point
in the direction of a unit vector
is given by:
where
is the gradient of
at
.First, we find the gradient of
:
Thus, the gradient is:
At the point
, the gradient is:
The given vector is
. We need to normalize it to get a unit vector:
The unit vector is
Now we compute the directional derivative:
Therefore, the directional derivative is
.Final Answer: The final answer is