<jupyter_start><jupyter_text>$\frac{\partial f}{\partial x} = 2\,\sqrt{a}\,x$<jupyter_code>import sympy
sympy.init_printing(use_latex = 'mathjax')
x = sympy.symbols('x')
x
type(x)
f = x * sympy.exp(x)
f
sympy.diff(f)
sympy.simplify(sympy.diff(f))
x, y = sympy.symbols('x y')
f = x ** 2 + x * y + y ** 2
f
sympy.diff(f, x)
sympy.diff(f, y)
x, mu , sigma = sympy.symbols('x mu sigma')
f = sympy.exp((x - mu) ** 2 / sigma ** 2)
f
sympy.diff(f, x)
sympy.simplify(sympy.diff(f, x))
!pip install tangent
import tangent

def f(x) :
    return x ** 3 - 3 * x ** 2 + x

import numpy as np
x = np.linspace(-1, 3, 10)

f(x)

fprime0 = tangent.grad(f)

fprime0(1)

fprime = np.vectorize(fprime0)

fprime(x)<jupyter_output><empty_output><jupyter_text>$$  \int 3x^2 dx $$$$ \int (3x^2 - 6x + 1)dx $$$$ \int \left( 2 + 6x + 4\exp(x) + \dfrac{5}{x} \right) dx $$$$ \int \frac{2x}{x^2 - 1} dx $$  $$\int \left( 1 + xy \right) dx  = x + \frac{1}{2}x^2 y  + C(y)$$$$\int \$$<jupyter_code>import numpy as np
import scipy as sp
import sklearn as sk

import matplotlib as mpl
mpl.use('Agg')
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D

%matplotlib inline
import sympy
sympy.init_printing(use_latex = 'mathjax')

def f(x) :
    return 3 * x**2 - 6 * x + 1

def f2(x) :
    return 2 + 6 * x + 4 * sympy.exp(x) + (5/x)
sp.integrate.quad(f, 0, 1)
sp.integrate.quad(f2, 1, 10)
def f3(x, y) :
    return 1 + x* y
sp.integrate.quad(f3, -1, 1)
import sympy
x, y = sympy.symbols('x y')
f = 1 + x * y
f

#부정 적분
F = sympy.integrate(f, x)
F
F2 = sympy.integrate(F, y)
F2
#성환님 답
x, y = sympy.symbols('x y')
f = 1+x*y
F = sympy.integrate(f, x)
F1 = sympy.integrate(F, y)
(F1.subs(x, 1) - F1.subs(x, -1)).evalf()<jupyter_output><empty_output>
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