Wichtige Ableitungen

$$f(x)=c \Rightarrow f'(x_0)=0$$

$$f(x)=m*x \Rightarrow f'(x_0)=m$$

$$f(x)=x^2 \Rightarrow f'(x_0)=2x_0$$

$$f(x)=x^3 \Rightarrow f'(x_0)=3x_0^2$$

$$f(x)=x^4 \Rightarrow f'(x_0)=4x_0^3$$

$$f(x)=\frac{1}{x}=x^{-1} \Rightarrow f'(x_0)=-\frac{1}{x_0^2}$$

$$f(x)=\sqrt{x}=x^{\frac{1}{2}} \Rightarrow f'(x_0)=\frac{1}{2\sqrt{x_0}}$$