1.4 differential

1.4.1 Derivative and differential

# The function is when you call matplotlib.pyplot The graph function of plot() When drawing ,
# Or generate a figure When it comes to canvases , It can be directly in your python console There's an image inside .
%matplotlib inline
from IPython import display
from mxnet import np, npx
from d2l import mxnet as d2l

npx.set_np()

# Defined function 
def f(x):
    return 3 * x ** 2 - 4 * x

# Find the limit 
def numerical_lim(f, x, h):
    return (f(x + h) - f(x)) / h

h = 0.1
for i in range(5):
    #print The string is preceded by f Represents a formatted string , Add f Variables and expressions enclosed in curly braces can be used in the string ,
    # If there is no expression in the string , So do you add it in front f The output should be the same .
    print(f'h={
      h:.5f}, numerical limit = {
      numerical_lim(f, 1, h):.5f}')
    h *= 0.1

h=0.10000, numerical limit = 2.30000
h=0.01000, numerical limit = 2.03000
h=0.00100, numerical limit = 2.00300
h=0.00010, numerical limit = 2.00030
h=0.00001, numerical limit = 2.00003

def use_svg_display(): #@save
    """ send ⽤svg Format in Jupyter Show in the middle ⽰ mapping ."""
    display.set_matplotlib_formats('svg')

def set_figsize(figsize = (3.5, 2.5)): #@save
    """ Set up matplotlib The chart ⼤⼩."""
    use_svg_display()
    d2l.plt.rcParams['figure.figsize'] = figsize

#@save
def set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend):
    """ Set up matplotlib The shaft ."""
    axes.set_xlabel(xlabel)
    axes.set_ylabel(ylabel)
    axes.set_xscale(xscale)
    axes.set_yscale(yscale)
    axes.set_xlim(xlim)
    axes.set_ylim(ylim)
    if legend:
        axes.legend(legend)
    axes.grid()

#@save
def plot(X, Y=None, xlabel=None, ylabel=None, legend=None, xlim=None,
         ylim=None, xscale='linear', yscale='linear',
         fmts=('-', 'm--', 'g-.', 'r:'), figsize=(3.5, 2.5), axes=None):
    """ Drawing data points ."""
    if legend is None:
        legend = []

    set_figsize(figsize)
    axes = axes if axes else d2l.plt.gca()
    
    #  If `X`  Yes ⼀ Axes , Output True
    def has_one_axis(X):
        return (hasattr(X, "ndim") and X.ndim == 1 or
            isinstance(X, list) and not hasattr(X[0], "__len__"))
    
    if has_one_axis(X):
        X = [X]
    if Y is None:
        X, Y = [[]] * len(X), X
    elif has_one_axis(Y):
        Y = [Y]
    if len(X) != len(Y):
        X = X * len(Y)
    axes.cla()
    for x, y, fmt in zip(X, Y, fmts):
        if len(x):
            axes.plot(x, y, fmt)
        else:
            axes.plot(y, fmt)
    set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend)

x = np.arange(0, 3, 0.1)
plot(x, [f(x), 2 * x - 3], 'x', 'f(x)', legend=['f(x)', 'Tangent line (x=1)'])

<ipython-input-15-80d5adcc870a>:3: DeprecationWarning: `set_matplotlib_formats` is deprecated since IPython 7.23, directly use `matplotlib_inline.backend_inline.set_matplotlib_formats()`
  display.set_matplotlib_formats('svg')

1.4.2 Partial derivative

1.4.3 gradient

1.4.4 The chain rule