大一高数 导数问题

y = 1/(x^2 + 5x + 6) = 1/(x + 2) - 1/(x + 3)

y^(100) = 100!/(x + 2)^101 - 100!/(x + 3)^101

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Mathematica:

In[24]:= D[1/(x+2)-1/(x+3),{x,100}]
Out[24]= 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000/(2+x)^101-93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000/(3+x)^101

原式=4[1/（x+2）-1/（x+3）]
y^(100)=(2×3×4×...×100)[1/（x+2）^101-1/（x+3）^101]
=100![1/（x+2）^101-1/（x+3）^101]