# Math Help - Directional derivative...

1. ## Directional derivative...

Consider a function at the point .
At that point the function has directional derivatives:
in the direction (parallel to) , and
in the direction (parallel to) . The gradient of at the point is?

2. Originally Posted by iwonder
Consider a function at the point .
At that point the function has directional derivatives:
in the direction (parallel to) , and
in the direction (parallel to) . The gradient of at the point is?
You have to solve the simultaneous equations:

$\frac{(u,v).(7,1)}{|(7,1)|}=\frac{5}{\sqrt{50}}$

$\frac{(u,v).(6,2)}{|(6,2)|}=\frac{5}{\sqrt{40}}$

where:

$
(u,v)= \left. \nabla f({\bf{x}})\right|_{{\bf{x}}={(6,1)}}
$

CB