Question Number 222284 by klipto last updated on 21/Jun/25
$$\boldsymbol{\mathrm{y}}=\frac{\mathrm{8}^{\boldsymbol{\mathrm{x}}} }{\left(\boldsymbol{\mathrm{in}}\mathrm{8}\right)^{\mathrm{3}} } \\ $$$$\boldsymbol{\mathrm{find}}\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{6}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{6}} } \\ $$
Answered by mr W last updated on 22/Jun/25
$${y}=\frac{{e}^{{x}\mathrm{ln}\:\mathrm{8}} }{\left(\mathrm{ln}\:\mathrm{8}\right)^{\mathrm{3}} } \\ $$$${y}^{\left(\mathrm{6}\right)} =\frac{\left(\mathrm{ln}\:\mathrm{8}\right)^{\mathrm{6}} {e}^{{x}\mathrm{ln}\:\mathrm{8}} }{\left(\mathrm{ln}\:\mathrm{8}\right)^{\mathrm{3}} }=\left(\mathrm{ln}\:\mathrm{8}\right)^{\mathrm{3}} \mathrm{8}^{{x}} \\ $$