Find directional derivative of $f(x,y) = e^x.cos(2x+y)$ at the point $(0,1)$ in the direction of the line $y = 3x + 1$
This is the question. I know how to solve it with vectors but when it comes to lines I couldn't understand how to do it. Besides, how can that "line" represents a line rather than a plane in 3 dimensional space? Thanks in advance.
Because the line has slope $3$. For every $3$ you rise in the $y$ direction you run $1$ in the $x$ direction. So the direction vector, the vector in the direction of the line, is $\langle 1,3 \rangle$. We are only concerned with $2$ dimensional direction when looking at direction vectors in $3$ dimensions. The meaning of direction vectors in $3$ D ($z=f(x,y)$) is the instantaneous rate of change in $z$ as move along the $xy$ plane in a certain direction from a point a certain amount of units.