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Math Help - Find the directional derivative??? help

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    Find the directional derivative??? help

    Find the directional derivative of f at the given point in the direction
    indicated by the angle theta.

    a) f(x, y) = (x^2 − y)^3, (3, 1), theta = 3pi/4.

    b) f(x, y) = sin(x + 2y), (4,−2), theta = −2pi/3.
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  2. #2
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    Quote Originally Posted by waterboy1203 View Post
    Find the directional derivative of f at the given point in the direction
    indicated by the angle theta.

    a) f(x, y) = (x^2 − y)^3, (3, 1), theta = 3pi/4.

    b) f(x, y) = sin(x + 2y), (4,−2), theta = −2pi/3.
    \frac{\partial f}{\partial l} = \nabla f \cdot \hat{l} where \hat{l} is a unit vector in the required direction.

    What part of this definition are you having trouble with.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by waterboy1203 View Post
    Find the directional derivative of f at the given point in the direction
    indicated by the angle theta.

    a) f(x, y) = (x^2 − y)^3, (3, 1), theta = 3pi/4.

    b) f(x, y) = sin(x + 2y), (4,−2), theta = −2pi/3.
    recall, the directional derivative of a function f at the point (x,y) in the direction of a unit vector \bold{u} = \left< a,b \right> is given by

    D_u(x,y) = \nabla f \cdot \bold{u} = f_x(x,y)a + f_y(x,y)b

    now, our problem here is finding the unit vector. if you are completely lost, just draw a diagram with the unit circle to figure out the vector that points in the direction you want. recall, therefore, that unit vectors in the direction \theta are given by \left< \cos \theta , \sin \theta \right>
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