# A Visual Introduction to Differentiation (using vpython)

#### Posted October 15, 2015

#### by Lensyl Urbano

This quick program is intended to introduce differentiation as a way of finding the slope of a line. Students know how to find the slope of a tangent line at least conceptually (by drawing). We pick a curve: in this case:

then enter values of x in the program to see how x, the function value and the differential compare to each other.

x | f(x) | f'(x) |
---|---|---|

0.5 | 0.25 | 1 |

1 | 1 | 2 |

2 | 2 | 4 |

3 | 9 | 6 |

Because it’s quick you have to change the function in the code, and enter the values for x in the python shell.

*differentiation_intro_numeric.py*

from visual import * class tangent_line: def __init__(self): self.dx = 0.1 self.line = curve() self.tangent_line = curve() self.point = sphere(radius=.25,color=color.yellow) self.point.visible = False self.label = label(pos=(-5,-8)) '''CHANGE FUNCTION (y) HERE''' # the original function def f(self, x): #y = sin(x) y = x**2 return y '''END CHANGE FUNCTION HERE''' def find_slope(self, x): sdx = .00001 m = (self.f(x+sdx)-self.f(x))/sdx return round(m,3) def draw(self): for x in arange(xmin, xmax+self.dx, self.dx): self.line.append(pos=(x, self.f(x))) def draw_tangent(self, x): m = self.find_slope(x) y = self.f(x) b = y - m * x print "When x = ", x, " slope = ", m self.label.text = "point: (%1.2f, %1.2f)\nSlope: %1.2f" % (x,y,m) self.plot_point(x) #draw tangent self.tangent_line.visible = False self.tangent_line = curve(pos=[(xmin,m*xmin+b),(xmax,m*xmax+b)], color=color.yellow) def plot_point(self, x): self.point.visible = True self.point.pos = (x, self.f(x)) #axes xmin = -10. xmax = 10. ymin = -10. ymax = 10. xaxis = curve(pos=[(xmin,0),(xmax,0)]) yaxis = curve(pos=[(0,ymin),(0,ymax)]) #tick marks tic_dx = 1.0 tic_h = .5 for i in arange(xmin,xmax+tic_dx,tic_dx): tic = curve(pos=[(i,-0.5*tic_h),(i,0.5*tic_h)]) for i in arange(ymin,ymax+tic_dx,tic_dx): tic = curve(pos=[(-0.5*tic_h,i),(0.5*tic_h,i)]) #stop scene from zooming out too far when the curve is drawn scene.autoscale = False # draw curve func = tangent_line() func.draw() # get input while 1: xin = raw_input("Enter x value: ") func.draw_tangent(float(xin))

**Citing this post**: **Urbano**, L., 2015. A Visual Introduction to Differentiation (using vpython), Retrieved September 26th, 2017, from *Montessori Muddle*: http://MontessoriMuddle.org/ .**Attribution (Curator's Code )**: Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.