```
%matplotlib inline
from sympy import *
init_printing()
```


```
x = symbols('x')
f = sqrt(1+x) - sqrt(1-x)
f
```


```
f_strich = simplify(diff(f, x))
f_strich
```


```
krel = Abs(expand(f_strich * x / f))
krel
```

    /usr/lib/python3.3/site-packages/IPython/core/formatters.py:239: FormatterWarning: Exception in image/png formatter: 
    \left\lvert{\frac{x}{2 x + 2 \sqrt{- x + 1} \sqrt{x + 1} - 2} + \frac{x}{2 x - 2 \sqrt{- x + 1} \sqrt{x + 1} + 2}}\right\rvert
         ^
    Expected a delimiter (at char 5), (line:1, col:6)
      FormatterWarning,





$$\left\lvert{\frac{x}{2 x + 2 \sqrt{- x + 1} \sqrt{x + 1} - 2} + \frac{x}{2 x - 2 \sqrt{- x + 1} \sqrt{x + 1} + 2}}\right\rvert$$




```
krel_daniel = x**2 / 2 * 1 / (sqrt(1-x**2)-(1-x**2))
krel_daniel
```


```
simplify(krel_daniel-krel)
```

    /usr/lib/python3.3/site-packages/IPython/core/formatters.py:239: FormatterWarning: Exception in image/png formatter: 
    \frac{1}{x^{2} + \sqrt{- x^{2} + 1} - 1} \left(x^{2} / 2 - \left(x^{2} + \sqrt{- x^{2} + 1} - 1\right) \left\lvert{\frac{x^{2}}{\left(x - \sqrt{- x + 1} \sqrt{x + 1} + 1\right) \left(x + \sqrt{- x + 1} \sqrt{x + 1} - 1\right)}}\right\rvert\right)
                                                                                                                ^
    Expected a delimiter (at char 108), (line:1, col:109)
      FormatterWarning,





$$\frac{1}{x^{2} + \sqrt{- x^{2} + 1} - 1} \left(\frac{x^{2}}{2} - \left(x^{2} + \sqrt{- x^{2} + 1} - 1\right) \left\lvert{\frac{x^{2}}{\left(x - \sqrt{- x + 1} \sqrt{x + 1} + 1\right) \left(x + \sqrt{- x + 1} \sqrt{x + 1} - 1\right)}}\right\rvert\right)$$




```
plot(krel, (x, -1/2, 1/2))
```


```
plot(krel_daniel, (x, -1/2, 1/2))
```


```

```

82463130d330096f221b7035a33720161adc0381
ipynb
Jupyter Notebook
Aufgabe 5c).ipynb
bschwb/Numerik
dcd178847104c382474142eae3365b6df76d8dbf
MIT
Aufgabe 5c).ipynb
bschwb/Numerik
dcd178847104c382474142eae3365b6df76d8dbf
MIT
Aufgabe 5c).ipynb
bschwb/Numerik
dcd178847104c382474142eae3365b6df76d8dbf
MIT
Qwen/Qwen-72B
1. YES
2. YES