Suppose we differentiate over again, we shall get the “second derived function” or second differential coefficient, which is denoted by ; and so on.
Now let us generalize.
Let .
First differentiation,
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Second differentiation,
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Third differentiation,
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Fourth differentiation,
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etc., etc.
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But this is not the only way of indicating successive differentiations. For,
if the original function be ;
once differentiating gives ;
twice differentiating gives ;
and this is more conveniently written as , or more usually . Similarly, we may write as the result of thrice differentiating, .