How can I find the directional derivative of F(x,y...

How can I find the directional derivative of F(x,y,z) =x-(y^2)+3xz at the point (1,2,3) in the direction paralle to(2,-1,-5) ?
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How can I find div F and curl F in the given F(x,y,z) =(2x,3xy,(x^2)-y)?
  
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How can I prove that g (x,y)=3x(y^3) is differentiable usingthe definition of diferentiability?

Answers ( 2 )

  1. esat adal
    esat adal
    Thank you for your response.
    Could you also help me with the last question please?
    Thanks,
  2. tristan fortin
    tristan fortin
    (a)
    Then
    and thus
    The given vector is not a unit vector.First we find a unitvector in the direction of this vector which is say u=
    Thus the directional derivative in the direction of givenvector is:

    (b)
                                                                          
                  
    Similarly find
                                    
                                     

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