```python
from sympy import init_session
init_session()
```

    IPython console for SymPy 1.6 (Python 3.7.3-64-bit) (ground types: python)
    
    These commands were executed:
    >>> from __future__ import division
    >>> from sympy import *
    >>> x, y, z, t = symbols('x y z t')
    >>> k, m, n = symbols('k m n', integer=True)
    >>> f, g, h = symbols('f g h', cls=Function)
    >>> init_printing()
    
    Documentation can be found at https://docs.sympy.org/1.6/
    



```python
# this is for rac[4,2]
a, b, d, e, k, l0 = symbols('a b d e k l0', real=True, positive=True)
```


```python
A, B, D, E = a**2, b**2, d**2, e**2
TA = 2*A
A2B = A*A + B
    
f1 = k**2 + TA*k + A2B
f2 = 1 + D*k
den = A2B + k*(TA + D*(A2B)) + E*k**2
f= l0 * f1 * f2 /den
f.factor()
```


```python
diff(f,l0)
```


```python
da=diff(f,a)
da.factor()
```


```python
db=diff(f,b)
db.factor()
```


```python
dd=diff(f,d)
dd.factor()
```


```python
de=diff(f,e)
de.factor()
```


```python

```

3d51c2fbead7a0f4cfd9d2f6daf6c2c3db13c85b
ipynb
Jupyter Notebook
notebooks/RAC-32_derivatives.ipynb
jeremydavis-2/Jolanta-by-dvr
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notebooks/RAC-32_derivatives.ipynb
jeremydavis-2/Jolanta-by-dvr
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notebooks/RAC-32_derivatives.ipynb
jeremydavis-2/Jolanta-by-dvr
025f7392ffc40c12ede2f07efefd1f2b0dcd8d35
Apache-2.0
Qwen/Qwen-72B
1. YES
2. YES