Was ist die Ableitung von x*(x+1)^-1
1. Methode:
f(x)=x⋅(x+1)−1
f(x)=u⋅vf′(x)=u⋅v′+u′⋅v
u=xv=(x+1)−1u′=1v′=(−1)(x+1)−2⋅1=−(x+1)−2f′(x)=x⋅[−1(x+1)−2]+1⋅(x+1)−1f′(x)=−x⋅(x+1)−2+(x+1)−1f′(x)=−x(x+1)2+1x+1f′(x)=−x(x+1)2+1x+1(x+1x+1)f′(x)=−x+x+1(x+1)2f′(x)=1(x+1)2
2. Methode:
f(x)=xx+1
f(x)=uvf′(x)=uv(u′u−v′v)
u=xv=x+1u′=1v′=1f′(x)=xx+1(1x−1x+1)f′(x)=xx+1(x+1−xx(x+1))f′(x)=xx+1(1x(x+1))f′(x)=1(x+1)2
Was ist die Ableitung von x*(x+1)^-1
1. Methode:
f(x)=x⋅(x+1)−1
f(x)=u⋅vf′(x)=u⋅v′+u′⋅v
u=xv=(x+1)−1u′=1v′=(−1)(x+1)−2⋅1=−(x+1)−2f′(x)=x⋅[−1(x+1)−2]+1⋅(x+1)−1f′(x)=−x⋅(x+1)−2+(x+1)−1f′(x)=−x(x+1)2+1x+1f′(x)=−x(x+1)2+1x+1(x+1x+1)f′(x)=−x+x+1(x+1)2f′(x)=1(x+1)2
2. Methode:
f(x)=xx+1
f(x)=uvf′(x)=uv(u′u−v′v)
u=xv=x+1u′=1v′=1f′(x)=xx+1(1x−1x+1)f′(x)=xx+1(x+1−xx(x+1))f′(x)=xx+1(1x(x+1))f′(x)=1(x+1)2