calculo - f(x)=ax b[a(x h β]−[ax β f(x)lim � h→0 h[ax ah β−ax−β f x)lim � h→0 h ah f(x)lim � h→0 h f(x = a 6 f(x)=x ❑2 x 1 ❑2 ❑2

calculo - f(x)=ax b[a(x h β]−[ax β f(x)lim � h→0...

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6) f(x)=ax+bf(x)limh→0¿[a(x+h)+β]−[ax+β]hf(x)limh→0¿[ax+ah+βaxβ]hf(x)limh→0¿ahhf(x)=a8) f(x)=x2+x+1f(x)limh→0¿x+h¿2+(x+h)+1−[x2+x+1]¿¿¿¿f(x)limh→0¿x2+2xh+h2+x+h+1x2x1hf(x)limh→0¿2x+h2+hhf(x)limh→0¿h(2x+h+1)hf(x)=¿2x+19)f(x)=a x2+bx+climh→0¿x+h¿2+b(x+h)+c−[ax2+bx+c]¿a¿¿¿limh→0¿[a x2+2axh+ah2+bx+bh+ca x2bxc]hlimh→0¿[+2axh+ah2+bh]hf ´(x)limh→0¿h[+2ax+ah+b]hf ´(x)limh→0¿2ax+ah+hxf ´¿)=2ax10)f(x)=x4f ´(x)limh→0¿x+h¿4−[x4]¿¿¿¿
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limh→0¿x4+4x3h+6x2h2+3x2❑❑h3+x h3+h4x4hlimh→0¿h(4x3+6x2+h❑❑+3x2❑❑h2+xh2+h3)hf ´(x)=¿4x3+6x211)f(x)=x3+2x2+1limh→0¿x+h¿3+2(x+h)+1−[x3+2x2+1]¿¿¿¿limh→0¿x3+3x3h+3x❑❑h3+h3+1x32x21hlimh→0¿3x3h+3x❑❑h3+h32x2hlimh→0¿h(3x3+3x❑❑h2+h22x2)hf ´(x)=3x32x212)g(X)=x4+x2limh→0¿x+h¿2−[x4+x2]¿x+h¿4+¿¿¿¿limh→0¿x4+4x3h+6x2h2+3x2❑❑h3+x h3+h4+x2+2xh+h2−[x4+x2]hlimh→0¿+4x3h+6x2h2+4x❑❑h3+h4+2xh❑❑+h2hlimh→0¿h4x3+6x2h❑❑+4x❑❑h2+h3+2x❑❑+¿¿¿h¿¿f ´(x)=4x3+2x13) h(X)=¿2x(x)=¿2x21(x)=¿2x3(x)=¿12x3
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14) s(x)=1x+1s ´(x)=limh→0¿(1(x+h+1))−(1x+1)limh→0¿(1(x+h+1))−(1x+1)hlimh→0¿(1(x+h+1))−(1x+1)(x+h+1)(x+1)hutilizamos ley de extremos y medios limh→0¿x+1xh1h(x+h+1)(x+1)x+1¿2¿s ´(X)=1¿15) f(x)=6x2+1x2+1¿2¿(f(x)g(x))´=0(x2+1)−6(2x)¿x2+1¿2¿f ´(x)=12x¿16) f(x)=x1x+1x❑❑+1¿2¿(f(x)g(x))´=(x1❑❑)(x❑❑+1)−(x1)(x1)¿x❑❑+1¿2¿f ´(x)=x+x1❑❑x+x1¿x❑❑+1¿2¿f ´(x)=2x1¿17)f(x)=2x1(x❑❑4)x❑❑4¿2¿f(x)=2x(x4)−(2x1)(x1)¿
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x❑❑4¿2¿f(x)=2x28x1+x1¿18)x2x¿❑❑¿g(x)=2x¿limh→0¿(2x(x2+hx))−(2xx2x)hlimh→0¿(2x)(x2x)−(2x)(x2x+h)(x2x+h)(x2x)limh→01h2x32x22x3+2x22xh¿¿¿limh→01h2xh(x2x+h)(x2x)limh→0¿2x(x2x)(x2x)x2
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