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from manimlib.imports import *
class Derivative(GraphScene):
CONFIG = {
"x_min": 0,
"x_max": 3,
"y_min": 0,
"y_max": 5,
"graph_origin": ORIGIN+6*LEFT+3*DOWN,
"x_axis_width": 6,
"x_labeled_nums": list(range(0, 4)),
"y_labeled_nums": list(range(0, 6)),
}
def construct(self):
XTD = self.x_axis_width/(self.x_max - self.x_min)
YTD = self.y_axis_height/(self.y_max - self.y_min)
self.setup_axes(animate = True)
graph = self.get_graph(lambda x : x*x, x_min = 0.5, x_max = 2, color = GREEN)
point1 = Dot().shift(self.graph_origin+0.25*YTD*UP + 0.5*XTD*RIGHT)
point1_lab = TextMobject(r"$t = a$")
point1_lab.scale(0.7)
point1_lab.next_to(point1, RIGHT)
point2 = Dot().shift(self.graph_origin+2*XTD*RIGHT+4*YTD*UP)
point2_lab = TextMobject(r"$t = b$")
point2_lab.scale(0.7)
point2_lab.next_to(point2, RIGHT)
vector1 = Arrow(self.graph_origin, self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, buff=0.02, color = RED)
vector1_lab = TextMobject(r"$\vec r(t)$", color = RED)
vector1_lab.move_to(self.graph_origin+1.2*XTD*RIGHT+ 0.75*YTD*UP)
vector1_lab.scale(0.8)
vector2 = Arrow(self.graph_origin, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = YELLOW_C)
vector2_lab = TextMobject(r"$\vec r(t + h)$", color = YELLOW_C)
vector2_lab.move_to(self.graph_origin+0.5*XTD*RIGHT+ 2*YTD*UP)
vector2_lab.scale(0.8)
vector3 = Arrow(self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = PINK)
vector3_lab = TextMobject(r"$\vec r(t + h) - \vec r(t)$", color = PINK)
vector3_lab.move_to(self.graph_origin+2*XTD*RIGHT+ 1.5*YTD*UP)
vector3_lab.scale(0.8)
self.play(ShowCreation(graph))
self.play(ShowCreation(point1), Write(point1_lab))
self.play(ShowCreation(point2), Write(point2_lab))
self.play(GrowArrow(vector1),Write(vector1_lab))
self.play(GrowArrow(vector2),Write(vector2_lab))
self.play(GrowArrow(vector3),Write(vector3_lab))
self.wait(1)
self.display_text()
self.play(ApplyMethod(vector3_lab.move_to,(self.graph_origin+2.3*XTD*RIGHT+ 2.2*YTD*UP)))
vector4 = Arrow(self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, self.graph_origin+1*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = PURPLE)
vector4_lab = TextMobject(r"$dx$", color = PURPLE)
vector4_lab.move_to(self.graph_origin+1.7*XTD*RIGHT+ 0.8*YTD*UP)
vector4_lab.scale(0.7)
vector5 = Arrow(self.graph_origin+1*YTD*UP + 1.5*XTD*RIGHT, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = ORANGE)
vector5_lab = TextMobject(r"$dy$", color = ORANGE)
vector5_lab.move_to(self.graph_origin+1.7*XTD*RIGHT+ 1.4*YTD*UP)
vector5_lab.scale(0.7)
self.play(GrowArrow(vector4),Write(vector4_lab))
self.play(GrowArrow(vector5),Write(vector5_lab))
self.wait(2)
def display_text(self):
text1 = TextMobject(r"$\vec r(t)$",r"+", r"$\vec r(t + h) - \vec r(t)$")
text1[0].set_color(RED)
text1[2].set_color(PINK)
text1.scale(0.7)
text2 = TextMobject(r"$\vec r(t + h)$", color = YELLOW_C)
text2.scale(0.7)
text3 = TextMobject(r"$ \vec r(t + h) - \vec r(t)$", color = PINK)
text3.scale(0.7)
text4 = TextMobject(r"[", r"$x(t+h)$", r"$\vec i$", r"+", r"$y(t+h)$", r"$\vec j$", r"$] - [$", r"$x(t)$", r"$\vec i$", r"+", r"y(t)", r"$\vec j$", r"]")
text4.set_color_by_tex(r"\vec i", BLUE)
text4.set_color_by_tex(r"\vec j", GREEN)
text4[1].set_color(YELLOW_C)
text4[4].set_color(YELLOW_C)
text4[-6].set_color(RED)
text4[-3].set_color(RED)
text4.scale(0.7)
text5 = TextMobject(r"$[x(t+h) - x(t)]$", r"$\vec i$", r"+", r"$[y(t+h) + y(t)]$", r"$\vec j$")
text5.set_color_by_tex(r"\vec i", BLUE)
text5.set_color_by_tex(r"\vec j", GREEN)
text5[0].set_color(PURPLE)
text5[3].set_color(ORANGE)
text5.scale(0.7)
text6 = TextMobject(r"$\frac{[\vec r(t + h) - \vec r(t)]}{h}$", r"=", r"$\frac{[x(t+h) - x(t)]}{h}$", r"$\vec i$", r"+", r"$\frac{[y(t+h) + y(t)]}{h}$", r"$\vec j$")
text6.set_color_by_tex(r"\vec i", BLUE)
text6.set_color_by_tex(r"\vec j", GREEN)
text6[0].set_color(PINK)
text6[2].set_color(PURPLE)
text6[-2].set_color(ORANGE)
text6.scale(0.8)
text7 = TextMobject(r"$\lim_{h \rightarrow 0}$", r"$\frac{[\vec r(t + h) - \vec r(t)]}{h}$", r"=", r"$\lim_{h \rightarrow 0}$", r"$\frac{[x(t+h) - x(t)]}{h}$", r"$\vec i$", r"+", r"$\lim_{h \rightarrow 0}$", r"$\frac{[y(t+h) + y(t)]}{h}$", r"$\vec j$")
text7.set_color_by_tex(r"\vec i", BLUE)
text7.set_color_by_tex(r"\vec j", GREEN)
text7[1].set_color(PINK)
text7[4].set_color(PURPLE)
text7[-2].set_color(ORANGE)
text7.scale(0.6)
text8 = TextMobject(r"$\vec r'(t)$", r"=",r"$\vec x'(t)$", r"$\vec i$", r"+", r"$\vec y'(t)$", r"$\vec j$")
text8.set_color_by_tex(r"\vec i", BLUE)
text8.set_color_by_tex(r"\vec j", GREEN)
text8[0].set_color(PINK)
text8[2].set_color(PURPLE)
text8[5].set_color(ORANGE)
text8.scale(0.7)
text9 = TextMobject(r"$\frac{d \vec r}{dt}$", r"=", r"$\frac{d \vec x}{dt}$", r"$\vec i$", r"+", r"$\frac{d \vec y}{dt}$", r"$\vec j$")
text9.set_color_by_tex(r"\vec i", BLUE)
text9.set_color_by_tex(r"\vec j", GREEN)
text9[0].set_color(PINK)
text9[2].set_color(PURPLE)
text9[5].set_color(ORANGE)
text9.scale(0.7)
text10 = TextMobject(r"$d \vec r$", r"=", r"$\frac{d \vec x}{dt}dt$", r"$\vec i$", r"+", r"$\frac{d \vec y}{dt}dt$", r"$\vec j$")
text10.set_color_by_tex(r"\vec i", BLUE)
text10.set_color_by_tex(r"\vec j", GREEN)
text10[0].set_color(PINK)
text10[2].set_color(PURPLE)
text10[5].set_color(ORANGE)
text10.scale(0.7)
text11 = TextMobject(r"$d \vec r$", r"=", r"$x'(t)dt$", r"$\vec i$", r"+", r"$y'(t)dt$", r"$\vec j$")
text11.set_color_by_tex(r"\vec i", BLUE)
text11.set_color_by_tex(r"\vec j", GREEN)
text11[0].set_color(PINK)
text11[2].set_color(PURPLE)
text11[5].set_color(ORANGE)
text11.scale(0.7)
text12 = TextMobject(r"$d \vec r$", r"=", r"$dx$", r"$\vec i$", r"+", r"$dy$", r"$\vec j$")
text12.set_color_by_tex(r"\vec i", BLUE)
text12.set_color_by_tex(r"\vec j", GREEN)
text12[0].set_color(PINK)
text12[2].set_color(PURPLE)
text12[5].set_color(ORANGE)
text12.scale(0.7)
text1.move_to(1*UP+2.7*RIGHT)
text2.move_to(1*UP+2.7*RIGHT)
text3.move_to(1*UP+2.7*RIGHT)
text4.move_to(1*UP+2.7*RIGHT)
text5.move_to(1*UP+2.7*RIGHT)
text6.move_to(1*UP+2.7*RIGHT)
text7.move_to(1*UP+2.5*RIGHT)
text8.move_to(1*UP+2.7*RIGHT)
text9.move_to(1*UP+2.7*RIGHT)
text10.move_to(1*UP+2.7*RIGHT)
text11.move_to(1*UP+2.7*RIGHT)
text12.move_to(1*UP+2.7*RIGHT)
brace1 = Brace(text7[0:2], DOWN, buff = SMALL_BUFF)
brace2 = Brace(text7[3:6], UP, buff = SMALL_BUFF)
brace3 = Brace(text7[7:], DOWN, buff = SMALL_BUFF)
t1 = brace1.get_text(r"$\vec r'(t)$")
t1.set_color(PINK)
t2 = brace2.get_text(r"$\vec x'(t)$")
t2.set_color(PURPLE)
t3 = brace3.get_text(r"$\vec y'(t)$")
t3.set_color(ORANGE)
self.play(Write(text1))
self.play(Transform(text1, text2))
self.wait(1)
self.play(Transform(text1, text3))
self.wait(1)
self.play(Transform(text1, text4))
self.wait(1)
self.play(Transform(text1, text5))
self.wait(1)
self.play(Transform(text1, text6))
self.wait(1)
self.play(Transform(text1, text7))
self.wait(1)
self.play(
GrowFromCenter(brace1),
FadeIn(t1),
)
self.wait()
self.play(
ReplacementTransform(brace1.copy(),brace2),
ReplacementTransform(t1.copy(),t2)
)
self.wait()
self.play(
ReplacementTransform(brace2.copy(),brace3),
ReplacementTransform(t2.copy(),t3)
)
self.wait()
self.play(FadeOut(brace1), FadeOut(t1), FadeOut(brace2), FadeOut(t2), FadeOut(brace3), FadeOut(t3),)
self.wait()
self.play(Transform(text1, text8))
self.wait(1)
self.play(Transform(text1, text9))
self.wait(1)
self.play(Transform(text1, text10))
self.wait(1)
self.play(Transform(text1, text11))
self.wait(1)
self.play(Transform(text1, text12))
self.wait(1)
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