2122_SA3_1
$f'(x)=\frac{x-2}{2x^3}$
2122_SA3_2
$f'(x)=\left(2+2x-4x^2\right)\cdot e^{1-x^2}$
2122_SA3_3
$\otimes \; f'(x)+g'(x)$
2122_B_6.2.1
$f'(x)=24\cdot x^2\cdot \cos\left(4x^3\right)$
$g'(x)=\frac{-2x^2+2x+8}{\left(x^2+4\right)^2}=\frac{-2x^2+2x+8}{x^4+8x^2+16}$
2122_B_6.2.2
- $\left( f(x)+g(x)\right)’=2-\sin(x)$
- $\left( f(x)\cdot g(x) \right)’=2\cdot \cos(x)-2x\cdot \sin(x)$
2122_B_6.2.3
$x=\frac{a}{2}$. Hauptbedingung: $f_1(x)=2a^2+(a-x)^2+x^2$
2122_B_6.3.1
Definitionsmenge
$\mathbb{D}=\mathbb{R} \setminus \{ \frac{4}{3} \} $
Polstelle
$x=\frac{4}{3}$
Monotonie
- streng monoton steigend in $ \left] -\infty ; 0.203 \right] $ und $\left] 2.464; \infty \right[$
- streng monoton fallend in $ \left[ 0.203;\frac{4}{3} \right] $ und $\left[ \frac{4}{3}; 2.464\right]$
2122_B_6.3.2
Definitionsmenge
$\mathbb{D}=\mathbb{R} \setminus \{ 1 \} $
Polstelle
$x=1$
Monotonie
- streng monoton steigend in $ \left] -\infty ; 1 \right] $ und $\left] 1.678; \infty \right[$
- streng monoton fallend in $ \left[ 1;1.678 \right] $