Original
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
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Solving for {{MATH_34}} we see
{{MATH_35}}
This is what we have written above.
{{CMD_36}}
{{CMD_37}}