Consider the function $f(x,y) = 3x^{3}y-3xy^{4}$. Find the gradient of $f$:
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Find the gradient of $f$ at the point (-3, 1).
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Find the rate of change of the function $f$ at the point (-3, 1) in the direction $\mathbf u = \left\langle \frac{-2}{10}, \frac{\sqrt{96}}{10} \right\rangle$.