y=(1)/(1-x), n=3
Veja:
y'=[(1)'(1-x)-(1)(1-x)']/
/(1-x)²
y'=[0.(1-x)-(1)(-1)]/
/(1-2x+2x²)
y'=[0+1]/(1-2x+2x²)
y'=1/(1-2x+2x²)
y''=[1'(1-2x+2x²)-1.(1-2x+2x²)']/
/(1-2x+2x²)²
y''=[0.(1-2x+2x²)-1.(-2+4x)]/
y''=[2-4x]/(1-4x+8x²-8x³+4x^4)
y'''=[(2-4x)'(1-4x+8x²-8x³+4x^4)-
(2-4x)(1-4x+8x²-8x³+4x^4)'/
/(1-4x+8x²-8x³+4x^4)²
y'''=[-4(1-4x+8x²-8x³+4x^4)-
(2-4x)(-4+16x-24x²+16x³)/
/(1-4x+8x²-8x³+4x^4)².
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Verified answer
Veja:
y=(1)/(1-x), n=3
y'=[(1)'(1-x)-(1)(1-x)']/
/(1-x)²
y'=[0.(1-x)-(1)(-1)]/
/(1-2x+2x²)
y'=[0+1]/(1-2x+2x²)
y'=1/(1-2x+2x²)
y''=[1'(1-2x+2x²)-1.(1-2x+2x²)']/
/(1-2x+2x²)²
y''=[0.(1-2x+2x²)-1.(-2+4x)]/
/(1-2x+2x²)²
y''=[2-4x]/(1-4x+8x²-8x³+4x^4)
y'''=[(2-4x)'(1-4x+8x²-8x³+4x^4)-
(2-4x)(1-4x+8x²-8x³+4x^4)'/
/(1-4x+8x²-8x³+4x^4)²
y'''=[-4(1-4x+8x²-8x³+4x^4)-
(2-4x)(-4+16x-24x²+16x³)/
/(1-4x+8x²-8x³+4x^4)².
-1
0
0
nada mais simples