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Math Help - Rate of Change as moving toward a point

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    Rate of Change as moving toward a point

    Find the rate of change of f(x,y,z) = ln(x+yz^2)-sin(y+z)+xe^y at the point (0,1,-1) as you move toward the point (4,1,2)
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by crwhd4 View Post
    Find the rate of change of f(x,y,z) = ln(x+yz^2)-sin(y+z)+xe^y at the point (0,1,-1) as you move toward the point (4,1,2)
    you want the directional derivative here.

    first, find the vector from (0,1,-1) to (4,1,2).

    then find the unit vector in that direction

    then use the formula: D_u f = \nabla f \cdot u

    where \nabla f is the gradient vector of f (at the point (0,1,-1)), \cdot is the dot product and u is the unit vector i asked you to find.
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