If {{MATH_13}} is a differentiable function that is one-to-one near {{MATH_14}} and {{MATH_15}}, then {{CMD_16}} {{CMD_17}} {{MATH_18}} is {{CMD_19}}defined{{CMD_20}} for {{MATH_21}} near {{MATH_22}}, {{CMD_23}} {{MATH_24}} is {{CMD_25}}differentiable{{CMD_26}} near {{MATH_27}}, {{CMD_28}} last, but not least: {{MATH_29}} {{CMD_30}} {{CMD_31}} We will only explain the last result. We know {{MATH_32}} and now we use the chain rule to write {{ENV_33}} Solving for {{MATH_34}} we see {{MATH_35}} This is what we have written above. {{CMD_36}} {{CMD_37}}