oblicz pochodną x^{4} +4x^{3} + 3x^{2} / (x + 1)^{2}
x^{4} +4x^{3} + 3x^{2} / (x + 1)^{2}
pochodna
(4x^3+12x^2+6x)*(x+1)^2-(x^4+4x^3+3x^2)*2(x+1)
----------------------------------------------------------=
(x+1)^4
(4x^3+12x^2+6x)*(x^2+2x+1)-(x^4+4x^3+3x^2)*(2x+2)
-------------------------------------------------------------- =
4x^5+6x^4+4x^3+12x^4+24x^3+12x^2+6x^3+12x^2+6x-2x^5-2x^4-8x^4-8x^3-6x^3-6x^2
--------------------------------------------------------------------------------------------------- =
2x^5+8x^4+20x^3+18x^2+6x
---------------------------------
Dalej się skrócić już raczej nie da.
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x^{4} +4x^{3} + 3x^{2} / (x + 1)^{2}
pochodna
(4x^3+12x^2+6x)*(x+1)^2-(x^4+4x^3+3x^2)*2(x+1)
----------------------------------------------------------=
(x+1)^4
(4x^3+12x^2+6x)*(x^2+2x+1)-(x^4+4x^3+3x^2)*(2x+2)
-------------------------------------------------------------- =
(x+1)^4
4x^5+6x^4+4x^3+12x^4+24x^3+12x^2+6x^3+12x^2+6x-2x^5-2x^4-8x^4-8x^3-6x^3-6x^2
--------------------------------------------------------------------------------------------------- =
(x+1)^4
2x^5+8x^4+20x^3+18x^2+6x
---------------------------------
(x+1)^4
Dalej się skrócić już raczej nie da.