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 ${\delta }_y=\sqrt{{\left({\delta }_x\frac{\partial \left(x^C\right)}{\partial x}\right)}^2}=C{\delta }_x{x}^{C-1}$