Find the line tangent to the surface given by the function at the specified point $P$ in the direction of the vector $\vec { u }$ $f ( x , y ) = \cos ( x ) + \sin \left( y ^ { 2 } \right) , P = ( \pi , \sqrt { \pi } ) , \vec { u } = \left\langle \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right\rangle$

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The Answer of Find the line tangent to the surface given by the function at the specified point $P$ in the direction of the vector $\vec { u }$ $f ( x , y ) = \cos ( x ) + \sin \left( y ^ { 2 } \right) , P = ( \pi , \sqrt { \pi } ) , \vec { u } = \left\langle \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right\rangle$

Find the Line Tangent to the Surface Given by the Function