qoutient-regel-bsp

$$||"id":1495987931||f(x)=\frac{3x+x^2}{x-1}{u}^{\prime }(x)=3+2x{v}^{\prime }(x)=1f^{\prime }(x)=(3+2x)\ast (x-1)-\frac{(1)\ast (3x+x^2)}{(x-1{)}^2}=\frac{(3+2x)\ast (x-1)-3-x^2}{(x-1{)}^2}$$

3.50) a)

$$||"id":1686509877931||f(x)=\frac{x^2+1}{x}{f}^{\prime }(x)=\frac{2x\ast x-1\ast (x^2+1)}{x^2}=\frac{2x^2-x^2-1}{x^2}=\frac{x^2-1}{x^2}$$

b)

$$||"id":473356564098||f(x)=(\frac{1}{x^2+1})f^{\prime }(x)=\frac{0\ast (x^2+1)-2x\ast 1}{(x^2+1{)}^2}=-\frac{2x}{(x^2+1{)}^2}$$

d)

$$||"id":1000157281422||f(x)=\frac{x}{e^x}{f}^{\prime }(x)=\frac{e^x\ast (1-x)}{e^x}=\frac{1-x}{e^x}$$

e)

$$||"id":1114203845978||f(x)=\frac{1}{\sin (x)}{f}^{\prime }(x)=\frac{0\ast \sin (x)-\cos (x)}{(\sin (x){)}^2}=\frac{\cos (x)}{(\sin (x){)}^2}$$