Find Partial Derivative

Question

Find the partial derivative of V = straight pi r2 h with respect to h. Give your answer in terms of a numerical value, using r = 12.2 and h = 68.6. Do not use scientific notation or include units.

Answer 1

The partial derivative of πr²h with respect to h is ∂(πr²h)/∂h equal to πr².

The partial derivative of πr²h with respect to r is ∂(πr²h)/∂r equal to 2πhr.

For (r, h) equal to (12.2, 68.6), ∂(πr²h)/∂h equal to πr² calculates to π(12.2)² or 467.5946506.

For (r, h) equal to (12.2, 68.6), ∂(πr²h)/∂r equal to 2πhr calculates to 2π(68.6)(12.2) or 5258.523447.

Here π is approximated as 3.141592654.