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Aus Online Mathematik Brückenkurs 2

We expand the quadratic expression as

f(x)=x2−12=x22−2x21+12=x4−2x2+1.

When the function is written in this form, it is easy to differentiate term by term,

f(x)=ddxx4−2x2+1=ddxx4−2ddxx2+ddx1=4x4−1−22x2−1+0=4x3−4x=4x(x2−1).