Let $f ( x , y , z ) = \sqrt { 2 x + 3 y - z }$ . Find the rate of change of $f$ at the point $( 1,1 , - 4 )$ in the direction $\mathbf { u }$ where $\mathbf { u }$ is a unit vector making an angle $\theta = 150 ^ { \circ }$ with $\nabla f$ .

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The Answer of Let $f ( x , y , z ) = \sqrt { 2 x + 3 y - z }$ . Find the rate of change of $f$ at the point $( 1,1 , - 4 )$ in the direction $\mathbf { u }$ where $\mathbf { u }$ is a unit vector making an angle $\theta = 150 ^ { \circ }$ with $\nabla f$ .

Let f(x,y,z)=2x+3y−zf ( x , y , z ) = \sqrt { 2 x + 3 y - z }f(x,y,z)=2x+3y−z​

Let $f ( x , y , z ) = \sqrt { 2 x + 3 y - z }$