Find the derivative of the function at P0 in the direction of u.
-$$f ( x , y ) = \tan ^ { - 1 } \frac { - 3 x } { y } , \quad P _ { 0 } ( - 7 , - 8 ) , \quad \mathbf { u } = 12 \mathbf { i } - 5 \mathbf { j }$$
A) $\frac { 393 } { 6565 }$
B) $\frac { 456 } { 6565 }$
C) $\frac { 27 } { 505 }$
D) $\frac { 477 } { 6565 }$

Question

Quizplus · Accepted Answer

The directional derivative is calculated using the gradient of the function and the unit vector in the direction of u. After computing the gradient and normalizing u, the dot product gives the derivative.

Find the Derivative of the Function at P0 in the Direction