Question

Given F(r,s,t)= -r(9s²+9t³), compute Fᵣₛₜ = _______

Answer 1

To compute Fᵣₛₜ, we take the third partial derivatives of the function F(r,s,t) = -r(9s²+9t³) with respect to r, s, and t. The final result after taking the partial derivatives in sequence is that Fᵣₛₜ equals 0.

Step-by-step explanation:

To compute Fᵣₛₜ, which represents the third partial derivative of the function F(r,s,t) = -r(9s²+9t³) with respect to r, s, and then t, we need to perform the following steps:

1. Take the partial derivative of F with respect to r, denoted as Fᵣ.
2. Next, take the partial derivative of Fᵣ with respect to s, resulting in Fᵣₛ.
3. Finally, take the partial derivative of Fᵣₛ with respect to t, which gives us Fᵣₛₜ.

Performing these calculations, we find:

1. Fᵣ = -9s² - 9t³
2. Fᵣₛ = -18s
3. Fᵣₛₜ = 0

Therefore, Fᵣₛₜ = 0.