General Engineering Introduction/Error Analysis/Calculus of Error/power proof

Multiplying by a Constant Proof

if $y=x^{C}$ then ${\delta _{y}}=C\delta _{x}x^{C-1}$

Algebra Proof

can not figure one out

Calculus Proof

start with the formula: dependent equals constant times independent
$y=x^{C}$
then $\delta _{y}={\sqrt {\left(\delta _{x}{\frac {\partial {\left(x^{C}\right)}}{\partial x}}\right)^{2}}}=C\delta _{x}x^{C-1}$