Qn.1: Find the directional derivative of (x, y, z) = 4xz³ − 3x²y² at a point P (2, -1, 2) in the direction of u = 2i − 3j + 6k.

Here are the solutions to the problems:

Qn.1: Find the directional derivative of $\phi (x, y, z) = 4xz^3 - 3x^2y^2$ at a point P $(2, -1, 2)$ in the direction of $\mathbf{u} = 2\mathbf{i} - 3\mathbf{j} + 6\mathbf{k}$.

The directional derivative of a scalar function $\phi$ in the direction of a unit vector $\hat{\mathbf{u}}$ is given by $D_{\hat{\mathbf{u}}} \phi = \nabla \phi \cdot \hat{\mathbf{u}}$.

Step 1: Calculate the gradient $\nabla \phi$.

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