Chapter 14: Partial Derivatives - Section 14.3 - Partial Derivatives - Exercises 14.3 - Page 807: 37

$h_p=sinΦcosθ$ $h_Φ=pcosΦcosθ$ $h_θ=-psinΦsinθ$

Take the first partial derivatives of the given function. When taking partial derivative with respect to Φ, treat Φ and θ as constants, with respect to Φ, treat Φ and θ as constants, and with respect to θ, treat p and Φ as constants: $h_p=sinΦcosθ$ $h_Φ=pcosΦcosθ$ $h_θ=-psinΦsinθ$