Consider a function of two variable x,y , is it possible to understand the geometric meaning of the gradient just by looking its definition(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \nabla f = \frac{\partial f}{\partial x} \hat{x} + \frac{\partial f}{\partial y} \hat{y} [/tex]

I can understand the geometric meaning by directional derivative

[tex] \nabla f \cdot \vec{u} [/tex] where u is unit vector

But I want to interpret gradient's geomecric meaning "just" by it's definition, could someone tell me how?

thanks a lot

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# Gradient's geometric meaning

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