# Write formulas for the indicated partial derivatives for the multivariable function. g(k, m) = k^3m^6 − 8km a)g_k b)g_m c)g_m|_(k=2)

Write formulas for the indicated partial derivatives for the multivariable function.
$g\left(k,m\right)={k}^{3}{m}^{6}-8km$
a)${g}_{k}$
b)${g}_{m}$
c)${g}_{m}{\mid }_{k=2}$
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Khribechy
$g\left(k,m\right)={k}^{3}{m}^{6}-8km$ (1)
a) ${g}_{k}=\frac{\partial }{\partial k}\left({k}^{3}{m}^{6}-8km\right)$
${g}_{k}=3{k}^{2}{m}^{6}-8m$
b) Now,
${g}_{m}=\frac{\partial }{\partial m}\left({k}^{3}{m}^{6}-8km\right)$
${g}_{m}=6{k}^{3}{m}^{5}-8k$
c) ${g}_{m}{\mid }_{k=2}=6x\left({21}^{3}{m}^{5}-8\cdot 2=6\cdot 8\cdot {m}^{5}-16$
$⇒{g}_{m}{\mid }_{k=2}=48{m}^{5}-16=16\left(3{m}^{5}-1\right)$
$⇒{g}_{m}{\mid }_{k=2}=16\left(3{m}^{5}-1\right)$