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Aus Online Mathematik Brückenkurs 2

We are to differentiate the expression two times, so we start by differentiating once. The quotient rule gives

ddxx1−x2=1−x22x1−x2−x1−x2=1−x211−x2−x1−x2

We determine the derivative 1−x2  by using the chain rule

=1−x21−x2−x121−x21−x2=1−x21−x2−x121−x2−2x

We simplify the result as far as possible, so as to make the second differentiation easier:

=1−x21−x2+x21−x2=1−x21−x21−x22+x21−x2=1−x21−x21−x2+x2=11−x232

The second derivative is:

d2dx2x1−x2=ddx11−x232=ddx1−x2−32=−231−x2−23−11−x2=−231−x2−52−2x=3x1−x2−52=3x1−x252