Find the derivative of the function at P0 in the direction of u.
-$$f ( x , y ) = 6 x - 7 y , \quad P _ { 0 } ( - 7 , - 2 ) , \quad u = 4 i - 3 j$$
A) $- \frac { 11 } { 5 }$
B) $\frac { 3 } { 5 }$
C) $\frac { 59 } { 5 }$
D) 9

Question

Quizplus · Accepted Answer

The directional derivative is the dot product of the gradient of $ f $ and the unit vector $ u $. The gradient is $ \nabla f = (6, -7) $. The unit vector $ u $ is $ \frac{1}{5}(4, -3) $. The dot product is $ 6 \times 4 + (-7) \times (-3) = 24 + 21 = 45 $. The directional derivative is $ \frac{45}{5} = 9 $.

Find the Derivative of the Function at P0 in the Direction