Find the Directional Derivative of the Function at P in the Direction

Multiple Choice

Find the directional derivative of the function at P in the direction of $\overrightarrow { \mathbf { v } } \text {. }$ $f ( x , y ) = x ^ { 5 } - y ^ { 5 } , P ( 5,4 ) , \quad \overrightarrow { \mathbf { v } } = \frac { \sqrt { 2 } } { 2 } ( \hat { \mathbf { i } } + \hat { \mathbf { j } } )$

A) $( 922.5 ) \sqrt { 2 }$
B) $( - 5,252.5 ) \sqrt { 2 }$
C) $( 1,845.0 ) \sqrt { 2 }$
D) $( 5,252.5 ) \sqrt { 2 }$
E) $( 1,677.5 ) \sqrt { 2 }$