If {{MATH_7}} is a differentiable function at {{MATH_8}}, then {{MATH_9}} is continuous at {{MATH_10}}. {{CMD_11}} To explain why this is true, we are going to use the following definition of the derivative {{MATH_12}} Assuming that {{MATH_13}} exists, we want to show that {{MATH_14}} is continuous at {{MATH_15}}, hence we must show that {{MATH_16}} Starting with {{MATH_17}} we multiply and divide by {{MATH_18}} to get {{ENV_19}} Since {{MATH_20}} we apply the Difference Law to the left hand side {{MATH_21}} and use continuity of a constant to obtain that {{MATH_22}} Next, we add {{MATH_23}} on both sides and get that {{MATH_24}} Now we see that {{MATH_25}}, and so {{MATH_26}} is continuous at {{MATH_27}}. {{CMD_28}} {{CMD_29}}