Suppose that $\displaystyle f(x,y)= \sin(2 x+ 7 y)$ is a function of two variables.

1. Find the gradient of $f(x,y).$
Answer: $\nabla f(x,y) =$

2. Evaluate the gradient at the point $P(-14,4).$
Answer: $\nabla f(-14,4) =$

3. Find the rate of change of $f(x,y)$ at $P$ in the direction of the vector $\mathbf{u} = \frac{1}{2}\left(\sqrt{3}\mathbf{i}-\mathbf{j}\right) .$
Answer: $D_{\mathbf{u}}\,f(-14,4) =$

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