cistG

2020-11-23

Write formulas for the indicated partial derivatives for the multivariable function.
$k\left(a,b\right)=3a{b}^{4}+8\left({1.4}^{b}\right)$
a) $\frac{\partial k}{\partial a}$
b) $\frac{\partial k}{\partial b}$
c) $\frac{\partial k}{\partial b}{\mid }_{a=3}$

Latisha Oneil

a) $\frac{\partial k}{\partial a}=\frac{\partial }{\partial a}\left[3a{b}^{4}+8\left({1.4}^{b}\right)\right]$
$\frac{\partial k}{\partial a}=3{b}^{4}+0=3{b}^{4}$
$\frac{\partial k}{\partial a}=3{b}^{4}$
b) $\frac{\partial k}{\partial b}=\frac{\partial }{\partial b}\left[3a{b}^{4}+8\left({1.4}^{b}\right)\right]$
$\frac{\partial k}{\partial b}=3a\cdot 4{b}^{9}+8\left({1.4}^{b}\right)\mathrm{log}\left(1\cdot 4\right)$
$\frac{\partial k}{\partial b}=12a{b}^{3}+8\mathrm{ln}\left(1.4\right)\left({1.4}^{b}\right)$
c) $\frac{\partial k}{\partial b}{\mid }_{a=3}=12\cdot 3{b}^{3}+8\mathrm{ln}\left(1.4\right)\left({1.4}^{b}\right)$
$\frac{\partial k}{\partial b}{\mid }_{a=3}=36{b}^{3}+8\mathrm{ln}\left(1.4\right)\left({1.4}^{b}\right)$

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