1. ## 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?

2. ## 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 $\displaystyle \phi=\phi(x,y,z)$. Then you can form a vector field $\displaystyle (\nabla \phi)(x,y,z)=\left( \frac{\partial \phi}{\partial x},\frac{\partial \phi}{\partial y},\frac{\partial \phi}{\partial z}\right)$ called the gradient of phi.

So it is not the derivative but it is deeply related

3. ## Re: Gradient of a function? Originally Posted by evthim 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?

4. ## Re: Gradient of a function?

I've just updated the question.

5. ## Re: Gradient of a function? Originally Posted by evthim 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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