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Math Help - Directional derivatives

  1. #1
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    Directional derivatives

    Need help with this question :

    The directional derivative of f(x,y,z) at the point P0 is greatest in the direction of v=i+j-k and has value 5sq.root(3) in this direction.What is the directional derivative of f at P0 in the direction of w=i+j ?

    Help will be appreciated. I have an exam day after tomorrow.
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  2. #2
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    Re: Directional derivatives

    Hey mrmaaza123.

    For the directional derivative there is a standard formula in terms of the dot product.

    Directional derivative - Wikipedia, the free encyclopedia

    For this we do grad(f) . v_hat (v_hat = i + j normalized)

    So you have to relate grad(f) . z_hat (z_hat = i + j - k) to grad(f) . v_hat but you know the norm of grad(f) . v_hat so using these relationships you should get the answer.
    Thanks from mrmaaza123
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  3. #3
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    Re: Directional derivatives

    Got it ! Thank you very much !
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