We measure that the edge length of a cube is {{MATH_1}}. However, our ruler only allows us an accuracy of {{MATH_2}}. Use differentials to estimate the potential error in the surface area which results from this potential error in measurement. {{CMD_3}} The surface area of the cube, {{MATH_4}}, is a function of the edge length {{MATH_5}}: {{MATH_6}}. {{CMD_7}} {{CMD_8}} We have to compute the differential of {{MATH_9}} at {{MATH_10}}. {{MATH_11}}. {{CMD_12}} {{CMD_13}} First, we have compute the derivative of {{MATH_14}}. {{MATH_15}}. {{CMD_16}} {{CMD_17}} Now we compute the the differential of {{MATH_18}} at {{MATH_19}}. {{MATH_20}}. {{CMD_21}} {{CMD_22}} We have to determine {{MATH_23}}. {{MATH_24}}. {{CMD_25}} {{CMD_26}} The potential error when we compute the surface area based on the measurement of the edge length is then given by {{MATH_27}}. {{CMD_28}} {{CMD_29}} The potential error is {{MATH_30}} {{CMD_31}}