Adding and subtracting proof
can not come up with one
start with the formula: dependent equals constant times independent y = x + z {\displaystyle y=x+z} then δ y = ( δ x ∂ ( x + z ) ∂ x ) 2 + ( δ z ∂ ( x + z ) ∂ z ) 2 = δ x 2 + δ z 2 {\displaystyle \delta _{y}={\sqrt {\left(\delta _{x}{\frac {\partial {\left(x+z\right)}}{\partial x}}\right)^{2}+\left(\delta _{z}{\frac {\partial (x+z)}{\partial z}}\right)^{2}}}={\sqrt {\delta _{x}^{2}+\delta _{z}^{2}}}}