```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
a, b, g, d, e, o, k, l0 = symbols('a b g d e o k l0', real=True, positive=True)
```


```python
ksq=k**2
A, B, G, D, E, O = a**2, b**2, g**2, d**2, e**2, o**2
TA = 2*A
A2B = A*A + B
C = TA + (G+E)*A2B
f1 = ksq + TA*k + A2B
f2 = 1 + G*k + D*ksq
f3 = 1 + E*k
den = A2B + C*k + O*ksq
f = l0*f1*f2*f3/den
f
```


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


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


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


```python
dg=diff(f,g)
dg.factor()
```


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


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


```python
do=diff(f,o)
dd.factor()
```

48f1c12b3e48d9b43f3c6db943558c61bb14eae6
ipynb
Jupyter Notebook
notebooks/RAC_gradients/RAC-52_derivatives.ipynb
tsommerfeld/L2-methods_for_resonances
acba48bfede415afd99c89ff2859346e1eb4f96c
MIT
notebooks/RAC_gradients/RAC-52_derivatives.ipynb
tsommerfeld/L2-methods_for_resonances
acba48bfede415afd99c89ff2859346e1eb4f96c
MIT
notebooks/RAC_gradients/RAC-52_derivatives.ipynb
tsommerfeld/L2-methods_for_resonances
acba48bfede415afd99c89ff2859346e1eb4f96c
MIT
Qwen/Qwen-72B
1. YES
2. YES