0

0/12

### 13 Differentialrechnung

0/12/2

#### 13.2 Ableitungsregeln

0/12/2/4

##### 13.2.4 Quotientenregel
 $y$ $=$ $\frac{u\left(x\right)}{v\left(x\right)}$ $=$ $\frac{u}{v}$ ${y}^{\prime }$ $=$ $\frac{{u}^{\prime }\left(x\right)\cdot v\left(x\right)-u\left(x\right)\cdot {v}^{\prime }\left(x\right)}{{v}^{2}\left(x\right)}$ $=$ $\frac{{u}^{\prime }\cdot v-u\cdot {v}^{\prime }}{{v}^{2}}$

.
Beispiel 13 - 1:
 $y$ $=$ $\frac{{x}^{3}-4x+5}{2{x}^{2}-4x+1}$ $=$ $\frac{u}{v}$ $⇒$ ${y}^{\prime }$ $=$ $\frac{\stackrel{{u}^{\prime }}{\overbrace{\left(3{x}^{2}-4\right)}}\stackrel{v}{\overbrace{\left(2{x}^{2}-4x+1\right)}}-\stackrel{u}{\overbrace{\left({x}^{3}-4x+5\right)}}\stackrel{{v}^{\prime }}{\overbrace{\left(4x-4\right)}}}{\underset{{v}^{2}}{\underbrace{{\left(2{x}^{2}-4x+1\right)}^{2}}}}$
.