```python
from sympy import *
from sympy.abc import *
```


```python
ay, dy, q, F, L = symbols('A_{y} D_{y} q_{0} F L')

Dy = (2*q*L + 3*F)/4 
Ay = (2*q*L) + F - Dy
```


```python
m1 = -Ay*x + 2*q*L*(x-L)
m2 = m1 + F*(x-3*L)
m3 = m2 - Dy*(x-4*L)

U1 = integrate(m1, (x, 0, 2*L))
U2 = integrate(m2, (x, 2*L, 3*L))
U3 = integrate(m3, (x, 3*L, 4*L))
```


```python
Ut = (1/(2*E*I))*(U1 + U2 + U3)
Ut
```




$\displaystyle \frac{- 4 L^{3} q_{0} + 4 L^{2} \left(- \frac{F}{8} + \frac{L q_{0}}{4}\right) + 5 L^{2} \left(\frac{3 F}{8} + \frac{L q_{0}}{4}\right) + L \left(- 3 F L - 2 L^{2} q_{0}\right)}{2 E I}$




```python
deriv = Derivative(Ut, F).subs(F, 0)
deriv
```




$\displaystyle \left. \frac{\partial}{\partial F} \frac{- 4 L^{3} q_{0} + 4 L^{2} \left(- \frac{F}{8} + \frac{L q_{0}}{4}\right) + 5 L^{2} \left(\frac{3 F}{8} + \frac{L q_{0}}{4}\right) + L \left(- 3 F L - 2 L^{2} q_{0}\right)}{2 E I} \right|_{\substack{ F=0 }}$




```python
deriv.doit()
```




$\displaystyle - \frac{13 L^{2}}{16 E I}$




```python

```

c6072fdb61075697cdebd14c51a215b93194c6e7
ipynb
Jupyter Notebook
Projeto Zebra/Untitled.ipynb
Gabriel-Messia/Python
4f4946ce22bf14ef989c7ce807cd5e1c00338d80
MIT
Projeto Zebra/Untitled.ipynb
Gabriel-Messia/Python
4f4946ce22bf14ef989c7ce807cd5e1c00338d80
MIT
Projeto Zebra/Untitled.ipynb
Gabriel-Messia/Python
4f4946ce22bf14ef989c7ce807cd5e1c00338d80
MIT
Qwen/Qwen-72B
1. YES
2. YES