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diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py
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index 0000000..0a5832d
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+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py
@@ -0,0 +1,246 @@
+from manimlib.imports import *

+

+class PartialDerivX(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+

+        paraboloid = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                -2*2*np.sin(u)*np.sin(u)+2

+            ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],

+            resolution=(15, 32)).scale(1)

+

+        paraboloid_copy = paraboloid.copy()

+

+ 

+        paraboloid_x = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                -2*2*np.sin(u)*np.sin(u)+2

+            ]),u_min=0,u_max=PI/2,v_min=PI,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],

+            resolution=(15, 32)).scale(1)

+

+

+        parabola =ParametricFunction(

+                lambda u : np.array([

+                u,

+                0,

+                -(u*u) + 2

+            ]),color="#006400",t_min=-2,t_max=2,

+            )

+        

+        plane = Polygon(np.array([-2.2,0,-2.5]),np.array([2.2,0,-2.5]),np.array([2.2,0,2.5]),np.array([-2.2,0,2.5]),np.array([-2.2,0,-2.5]), color = GREEN, fill_color = GREEN, fill_opacity = 0.2)

+        plane_text = TextMobject(r"$y = 0$", color = GREEN_C).move_to(2*UP + 3*RIGHT)

+

+        surface_eqn = TextMobject("Surface", r"$z = f(x,y) = 2 - x^2 - y^2$", color = BLUE_C).scale(0.6).move_to(np.array([3*LEFT +3*UP]))

+        surface_eqn[0].set_color(PINK)

+

+        line = Line(np.array([-2,0,0]), np.array([2,0,0]), color = RED_C)

+        

+ 

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(3.7*UP)

+

+        self.add_fixed_in_frame_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+

+

+        self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)

+

+        self.play(Write(paraboloid))

+

+        self.add_fixed_in_frame_mobjects(surface_eqn)

+        #self.move_camera(phi=80* DEGREES,theta=95*DEGREES)

+        self.move_camera(phi=80* DEGREES,theta=45*DEGREES)

+        self.play(ShowCreation(plane))

+        self.add_fixed_in_frame_mobjects(plane_text)

+        self.wait()

+        self.play(ReplacementTransform(paraboloid, paraboloid_x))

+        self.play(FadeOut(plane), FadeOut(plane_text))

+        self.play(ShowCreation(parabola), ShowCreation(line))

+

+        text1 = TextMobject("Moving small", r"$dx$", r"steps").scale(0.6).move_to(3*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, BLUE, PURPLE)

+    

+        text2 = TextMobject("Observing change in function, keeping", r"$y$", r"constant").scale(0.6).move_to(2.6*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+        

+        slope_text = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "x}").scale(0.6).move_to(2*UP + 3.5*RIGHT)

+        slope_text[0].set_color(BLUE_E)

+        slope_text.set_color_by_tex("\\partial",PINK)

+        slope_text.set_color_by_tex("f","#006400")

+        slope_text[5].set_color(RED_C)

+

+        self.add_fixed_in_frame_mobjects(text1, text2)

+        self.wait()

+        self.add_fixed_in_frame_mobjects(slope_text)

+        #add_fixed_orientation_mobjects

+        

+        

+        dot = Dot().rotate(PI/2).set_color(RED_C)

+        alpha = ValueTracker(0)

+        vector = self.get_tangent_vector(alpha.get_value(),parabola,scale=1.5)

+        dot.add_updater(lambda m: m.move_to(vector.get_center()))

+        self.play(

+            ShowCreation(parabola),

+            GrowFromCenter(dot),

+            GrowArrow(vector)

+            )

+        vector.add_updater(

+            lambda m: m.become(

+                    self.get_tangent_vector(alpha.get_value()%1,parabola,scale=1.5)

+                )

+            )

+        self.add(vector,dot)

+        self.play(alpha.increment_value, 1, run_time=10, rate_func=linear)

+        self.wait()

+

+

+        '''

+        for i in np.arange(-2,2,0.2):

+            self.play(ReplacementTransform(Line(np.array([i,0,0]), np.array([i,0,-i*i + 2]), color = GREEN_C), Line(np.array([i+0.2,0,0]), np.array([i+0.2,0,-(i+0.2)**2 + 2]), color = GREEN_C)))

+            #self.wait()

+        '''

+

+        self.wait()

+        self.play(FadeOut(parabola), FadeOut(line), FadeOut(vector), FadeOut(dot), FadeOut(text1), FadeOut(text2), FadeOut(slope_text),FadeOut(surface_eqn))

+

+        #self.move_camera(phi=80* DEGREES,theta= 0*DEGREES)

+        self.play(ReplacementTransform(paraboloid_x, paraboloid_copy))

+        self.wait()

+

+

+    def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):

+        coord_i = curve.point_from_proportion(proportion)

+        coord_f = curve.point_from_proportion(proportion + dx)

+        reference_line = Line(coord_i,coord_f)

+        unit_vector = reference_line.get_unit_vector() * scale

+        vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = BLUE_E, buff=0)

+        return vector

+

+

+class PartialDerivY(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+

+        paraboloid = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                -2*2*np.sin(u)*np.sin(u)+2

+            ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],

+            resolution=(15, 32)).scale(1)

+

+        paraboloid_copy = paraboloid.copy()

+

+ 

+        paraboloid_y = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                -2*2*np.sin(u)*np.sin(u)+2

+            ]),u_min=0,u_max=PI/2,v_min=PI/2,v_max=3*PI/2,checkerboard_colors=[PINK, PURPLE],

+            resolution=(15, 32)).scale(1)

+

+

+        parabola =ParametricFunction(

+                lambda u : np.array([

+                0,

+                u,

+                -(u*u) + 2

+            ]),color=YELLOW_C,t_min=-2,t_max=2,

+            )

+        

+        plane = Polygon(np.array([0,-2.2,-2.5]),np.array([0,2.2,-2.5]),np.array([0,2.2,2.5]),np.array([0,-2.2,2.5]),np.array([0,-2.2,-2.5]), color = BLUE, fill_color = BLUE, fill_opacity = 0.2)

+        plane_text = TextMobject(r"$x = 0$", color = BLUE_C).move_to(2*UP + 3*RIGHT)

+

+        surface_eqn = TextMobject("Surface", r"$z = f(x,y) = 2 - x^2 - y^2$", color = BLUE_C ).scale(0.6).move_to(np.array([3*LEFT +3*UP]))

+        surface_eqn[0].set_color(PINK)

+        

+        line = Line(np.array([0,-2,0]), np.array([0,2,0]), color = RED_C)

+ 

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(3.7*UP)

+

+        self.add_fixed_in_frame_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+

+        self.set_camera_orientation(phi=80 * DEGREES, theta = 45*DEGREES)

+

+        self.play(Write(paraboloid))

+

+        self.add_fixed_in_frame_mobjects(surface_eqn)

+        #self.move_camera(phi=80* DEGREES,theta=5*DEGREES)

+        self.play(ShowCreation(plane))

+        self.add_fixed_in_frame_mobjects(plane_text)

+        self.wait()

+        self.play(ReplacementTransform(paraboloid, paraboloid_y))

+        self.play(FadeOut(plane), FadeOut(plane_text))

+        self.play(ShowCreation(parabola), ShowCreation(line))

+

+        text1 = TextMobject("Moving small", r"$dy$", r"steps").scale(0.6).move_to(3*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, BLUE, PURPLE)

+        

+        text2 = TextMobject("Observing change in function, keeping", r"$x$", r"constant").scale(0.6).move_to(2.6*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+        

+        slope_text = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "y}").scale(0.6).move_to(2*UP + 3.5*RIGHT)

+        slope_text[0].set_color("#006400")

+        slope_text.set_color_by_tex("\\partial",PINK)

+        slope_text.set_color_by_tex("f",YELLOW_C)

+        slope_text[5].set_color(RED_C)

+

+        self.add_fixed_in_frame_mobjects(text1, text2)

+        self.wait()

+        self.add_fixed_in_frame_mobjects(slope_text)

+

+        dot = Dot().rotate(PI/2).set_color(RED_C)

+        alpha = ValueTracker(0)

+        vector = self.get_tangent_vector(alpha.get_value(),parabola,scale=1.5)

+        dot.add_updater(lambda m: m.move_to(vector.get_center()))

+        self.play(

+            ShowCreation(parabola),

+            GrowFromCenter(dot),

+            GrowArrow(vector)

+            )

+        vector.add_updater(

+            lambda m: m.become(

+                    self.get_tangent_vector(alpha.get_value()%1,parabola,scale=1.5)

+                )

+            )

+        self.add(vector,dot)

+        self.play(alpha.increment_value, 1, run_time=10, rate_func=linear)

+        self.wait()

+        

+        '''

+        for i in np.arange(-2,2,0.2):

+            self.play(ReplacementTransform(Line(np.array([0,i,0]), np.array([0,i,-i*i + 2]), color = BLUE_C), Line(np.array([0,i+0.2,0]), np.array([0,i+0.2,-(i+0.2)**2 + 2]), color = BLUE_C)))

+            #self.wait()

+        '''

+

+

+        self.wait()

+        self.play(FadeOut(parabola), FadeOut(line), FadeOut(vector), FadeOut(dot), FadeOut(text1), FadeOut(text2), FadeOut(slope_text),FadeOut(surface_eqn))

+

+        #self.move_camera(phi=80* DEGREES,theta= 90*DEGREES)

+        self.play(ReplacementTransform(paraboloid_y, paraboloid_copy))

+        self.wait()   

+

+    def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):

+        coord_i = curve.point_from_proportion(proportion)

+        coord_f = curve.point_from_proportion(proportion + dx)

+        reference_line = Line(coord_i,coord_f)

+        unit_vector = reference_line.get_unit_vector() * scale

+        vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = "#006400", buff=0)

+        return vector         

+

+        
\ No newline at end of file