### Partial Derivatives of a Volume Function Compute the first-order partial derivatives of the function \( V = 15\pi r^2 h \). (Use symbolic notation and fractions where needed.) \[ \frac{\partial V}{\partial r} = \quad \_\_\_\_\_ \] \[ \frac{\partial V}{\partial h} = \quad \_\_\_\_\_ \] ### Explanation: This task requires finding the first-order partial derivatives of the given volume function \( V \) with respect to \( r \) (radius) and \( h \) (height). To compute \(\frac{\partial V}{\partial r}\), treat \( h \) as a constant and differentiate \( V = 15\pi r^2 h \) with respect to \( r \). To compute \(\frac{\partial V}{\partial h}\), treat \( r \) as a constant and differentiate \( V = 15\pi r^2 h \) with respect to \( h \). --- This detailed transcription would be suitable for learners who need to understand the process of calculating partial derivatives in calculus.