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Math Help - Gradient of a function?

  1. #1
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    Gradient of a function?

    Is the gradient of a function basically it's derivative?

    For instance, given f(x) = 3x^4 + 6x^2 + 7x + 3, the gradient of f(x) would be f'(x) = 12x^3 + 12x + 7, right?
    Last edited by evthim; April 1st 2013 at 09:44 AM.
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  2. #2
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    Re: Gradient of a function?

    The gradient of a (scalar) field is a vector field. Suppose you have a scalar field, such as a temperature field \phi=\phi(x,y,z). Then you can form a vector field (\nabla \phi)(x,y,z)=\left( \frac{\partial \phi}{\partial x},\frac{\partial \phi}{\partial y},\frac{\partial \phi}{\partial z}\right) called the gradient of phi.

    So it is not the derivative but it is deeply related
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    Re: Gradient of a function?

    Quote Originally Posted by evthim View Post
    Is the gradient of a function basically it's derivative?
    That are mathematics communities that do use the gradient of a function to mean it's derivative.
    So the answer to your question depends upon context.
    Can you be more forthcoming?
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    Re: Gradient of a function?

    I've just updated the question.
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    Re: Gradient of a function?

    Quote Originally Posted by evthim View Post
    I've just updated the question.
    Again, it depends on who is asking the question and in what course.
    In a basic calculus course then I would say that you are correct.
    But that is just a guess.
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