```python
# basic calculus

from sympy import *
x, y, z, t = symbols('x y z t')
init_printing(use_unicode=True)
```


```python
diff(x**2)
```


```python
diff(x**x)
```


```python
diff(cos(x)*sin(x)+exp(x)*sin(y) + cos(z)*exp(t))
```


```python
diff(cos(x)*sin(x)+exp(x)*sin(y) + cos(z)*exp(t), x)
```


```python
f = cos(x)*sin(x)+exp(x)*sin(y) + cos(z)*exp(t)
```


```python
f
```


```python
diff(f, x)
```


```python
dfx = diff(f, x)
simplify(dfx)
```


```python
integrate(f,x)
```


```python
intf = Integral(f,x)
```


```python
intf.doit()
```


```python
g = x**5
```


```python
diff(g)
```


```python
diff(g, x, 1)
```


```python
diff(g, x, 2)
```


```python
diff(g, x, x)
```


```python
diff(g, x, x, y)
```


```python
df = Derivative(g, x, x, y, y, t)
```


```python
df
```


```python
df.doit()
```


```python
# integration
```


```python
# indefinite integral
integrate(sin(x),x)
```


```python
# definite integral
integrate(exp(-x), (x, 0, oo))
```


```python
integrate(exp(-x**2-y**2), (x,-oo,oo), (y,0,oo) )
```


```python
intf = Integral(exp(-x**2-y**2), x)
```


```python
pprint(intf)
```

    ⌠              
    ⎮     2    2   
    ⎮  - x  - y    
    ⎮ ℯ          dx
    ⌡              



```python
# limits
limit(sin(x)/x, x, 0)
```


```python
# Taylor Series expansion
f = exp(x)
```


```python
f.series(x, 0, 4)
```


```python
f.series(x, 2, 4).removeO()
```


```python

```

8ebcbc36e8c97ca0878802d761c0d18591fd2337
ipynb
Jupyter Notebook
4-calculus-basic.ipynb
chennachaos/SA2CTechChatSymPy
9f1dbb48655ff5f8bdd6b4ced48b58aed0ba5bf4
MIT
4-calculus-basic.ipynb
chennachaos/SA2CTechChatSymPy
9f1dbb48655ff5f8bdd6b4ced48b58aed0ba5bf4
MIT
4-calculus-basic.ipynb
chennachaos/SA2CTechChatSymPy
9f1dbb48655ff5f8bdd6b4ced48b58aed0ba5bf4
MIT
Qwen/Qwen-72B
1. YES
2. YES