Final answer:
Without the explicit function for w in terms of r and θ, we cannot compute the partial derivatives. The procedure would involve evaluating the partial derivative of w with respect to r and with respect to θ at the given values.
Step-by-step explanation:
The information provided does not directly indicate a function for w in terms of r and θ (theta), so we cannot explicitly calculate the partial derivatives without the functional form of w. However, if we had a function w(r,θ), we would calculate the partial derivative with respect to r while keeping θ constant, and vice versa for the partial derivative with respect to θ.
Given a function w(r,θ), the partial derivative with respect to r evaluated at r = 4 and θ = 2 would be represented as \( \frac{\partial w}{\partial r}|_{r=4,\u03b8=2} \). Similarly, the partial derivative with respect to θ at those points would be \( \frac{\partial w}{\partial \u03b8}|_{r=4,\u03b8=2} \). Since we don't have the explicit function, we cannot calculate these values.