Question

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)

Multivariable functions
ANSWERED
asked 2021-02-27
Write formulas for the indicated partial derivatives for the multivariable function.
\(\displaystyle{g{{\left({k},{m}\right)}}}={k}^{{3}}{m}^{{6}}−{8}{k}{m}\)
a)\(\displaystyle{g}_{{k}}\)
b)\(\displaystyle{g}_{{m}}\)
c)\(\displaystyle{g}_{{m}}{\mid}_{{{k}={2}}}\)

Answers (1)

2021-02-28
\(\displaystyle{g{{\left({k},{m}\right)}}}={k}^{{3}}{m}^{{6}}−{8}{k}{m}\) (1)
a) \(\displaystyle{g}_{{k}}=\frac{\partial}{{\partial{k}}}{\left({k}^{{3}}{m}^{{6}}−{8}{k}{m}\right)}\)
\(\displaystyle{g}_{{k}}={3}{k}^{{2}}{m}^{{6}}−{8}{m}\)
b) Now,
\(\displaystyle{g}_{{m}}=\frac{\partial}{{\partial{m}}}{\left({k}^{{3}}{m}^{{6}}−{8}{k}{m}\right)}\)
\(\displaystyle{g}_{{m}}={6}{k}^{{3}}{m}^{{5}}−{8}{k}\)
c) \(\displaystyle{g}_{{m}}{\mid}_{{{k}={2}}}={6}{x}{\left({21}^{{3}}{m}^{{5}}-{8}\cdot{2}={6}\cdot{8}\cdot{m}^{{5}}-{16}\right.}\)
\(\displaystyle\Rightarrow{g}_{{m}}{\mid}_{{{k}={2}}}={48}{m}^{{5}}-{16}={16}{\left({3}{m}^{{5}}-{1}\right)}\)
\(\displaystyle\Rightarrow{g}_{{m}}{\mid}_{{{k}={2}}}={16}{\left({3}{m}^{{5}}-{1}\right)}\)
0
 
Best answer

expert advice

Need a better answer?
...