Word Count : 360

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To determine the directional derivative of the scalar field \[ \phi = \ln(x^2 + y^2 + z^2) \] at the point \( P(1, -1, 2) \) in the direction of \( \mathbf{v} = \hat{i} + 2\hat{j} - \hat{k} \), follow these steps: ### Step 1: Compute the Gradient \( \nabla \phi \) The gradient of \( \phi \) is given by: \[ \nabla \phi = \left( \frac{\partial \phi}{\partial x}, \frac{\partial \phi}{\partial y}, _________ __________ ________ ________ ____ __________ ___ _____ _______ ________.
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