(Solved): help me part a,b,c Your friend Jiaying wants to find the directional derivat ...

help me part a,b,c

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Your friend Jiaying wants to find the directional derivative of \[ \phi(x, y, z)=2 x^{2}-y^{3}+z^{4} \] at the point \( P(1,-1,1) \) in the direction of the outward-pointing normal vector of the surface \( \mathcal{S} \) at \( P \) where \( \mathcal{S} \) is giver by \[ \frac{x^{2}}{4}+\frac{y^{2}}{1}+\frac{z^{2}}{1}=9 / 4 \] Help Jiaying by answering the following questions. Syntax advice for part (a) and part (b): Your solution should be entered as a vector in Maple syntax and all entries should be entered as exact values. For example, if your answer is \( \left(\begin{array}{c}3 \\ 4 \\ 7 \\ -3\end{array}\right) \), then you should enter \( <3,4,7 /(-3)> \) (a) Find the gradient of \( \phi \). Enter your answer in the box below. \[ \nabla \phi= \] (b) Find an outward-pointing normal vector of \( \mathcal{S} \) at \( P \). \[ \mathbf{n}= \] (c) Find the directional derivative of \( \phi \) at \( P \) in the direction of \( \mathbf{n} \). Please enter your answer in exact form. Answer \( = \)