# Write formulas for the indicated partial derivatives for the multivariable function.g(k, m) = k^4m^5 − 3kma)g_kb)g_mc)g_m|_(k=2)

Write formulas for the indicated partial derivatives for the multivariable function.
$g\left(k,m\right)={k}^{4}{m}^{5}-3km$
a)${g}_{k}$
b)${g}_{m}$
c)${g}_{m}{\mid }_{k=2}$

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$g\left(k,m\right)={k}^{4}{m}^{5}-3km$ (1)
a) Differentiating with respect to x partially, we have
$\frac{\partial g}{\partial k}=\frac{\partial }{\partial k}\left[{k}^{4}{m}^{5}-3km\right]$
$⇒\frac{\partial g}{\partial k}=4{k}^{3}{m}^{5}-3m$
b) Differentiating with respect to x partially, we have
$\frac{\partial g}{\partial m}=\frac{\partial }{\partial m}\left[{k}^{4}{m}^{5}-3km\right]$
$⇒\frac{\partial g}{\partial m}=5{k}^{4}{m}^{4}-3k$
c) ${g}_{m}{|{}_{\left(k=2\right)}=\frac{\partial q}{\partial m}|}_{k=2}=5\cdot {\left(2\right)}^{4}{m}^{4}-3\cdot 2$
${g}_{m}{\mid }_{k=2}=80{m}^{4}-6$