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 $$\delta_y = \sqrt{\left ( \delta_x \frac{\partial {\left ( x^C \right )}} \right ) ^2} = C \delta_x x^{C-1}$$