Let $f ( x , y ) = \ln \sqrt { x ^ { 2 } + y ^ { 2 } }$

Multiple Choice

Let $f ( x , y ) = \ln \sqrt { x ^ { 2 } + y ^ { 2 } }$ . Then the directional derivative of f at (3,4) in the direction of the unit vector $\mathbf { U }$ which is parallel to $\mathbf { v } = 5 \mathbf { i } + 12 \mathbf { j }$ is

A) $\frac { \sqrt { 3 } + 1 } { 2 }$
B) $\sqrt { 15 }$
C) $- \frac { 7 } { 13 }$
D) $- \frac { 5 } { 13 }$
E) $\frac { 63 } { 325 }$