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Math Help - Directional derivative...

  1. #1
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    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?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by iwonder View Post
    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:

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

    CB
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