Question

given f(r,s,t)=r(9t^2 - 2s^4), compute: f_{rst}=

Explanation:

Step1: Find $F_r$

Treat $s$ and $t$ as constants. Using the power - rule for differentiation, if $F(r,s,t)=r(9t^{2}-2s^{4})=(9t^{2}-2s^{4})r$, then $F_r = 9t^{2}-2s^{4}$.

Step2: Find $F_{rs}$

Differentiate $F_r$ with respect to $s$ while treating $t$ as a constant. Since $F_r = 9t^{2}-2s^{4}$, then $F_{rs}=-8s^{3}$.

Step3: Find $F_{rst}$

Differentiate $F_{rs}$ with respect to $t$ while treating $s$ as a constant. Since $F_{rs}=-8s^{3}$ (a constant with respect to $t$), then $F_{rst} = 0$.

Answer:

$0$