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Math Help - grad vector field

  1. #1
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    grad vector field

    can someone please clarify for me what is the difference btw gradient vector field and directional derivative? im new to this topic and am completely lost:'(

    thanks so much!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by alexandrabel90 View Post
    can someone please clarify for me what is the difference btw gradient vector field and directional derivative? im new to this topic and am completely lost:'(

    thanks so much!
    The gradient is a vector: \nabla f\!\left(x,y,z\right)=\left<\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z}\right>

    The directional derivative is the dot product between your unit vector and the gradient: \nabla f\!\left(x,y,z\right)\cdot\mathbf{u}, which is a scalar quantity.

    Does this help?
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