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        formule4 = MathTex("\omega = \sum^{n}_{i = 1}", "f_i \cdot", " dx_1 \wedge ... \wedge \widehat {dx_i} \wedge ... \wedge dx_n").next_to(mprime2, DOWN, buff=SMALL_BUFF)
        formule4.shift(DOWN*0.5, RIGHT*0.3)
        self.play(Write(formule4))
        
        self.play(FadeOut(mprime2), FadeOut(mprime))
        self.play(formule4.animate.shift(LEFT*1.5))
        self.play(FadeOut(formule4[1]))
        formule4.remove([1])
        self.play(formule4[2].animate.shift(RIGHT*2.1))
        
        
        d = MathTex("d")
        d.next_to(formule4[0], LEFT, buff=SMALL_BUFF)
        d.shift(UP*0.05)
        formule4.add(d)
        
        new_expression = MathTex("(\sum^{n}_{j=1} \\frac {\partial f_i}{\partial x_j} dx_j)")
        new_expression.next_to(formule4[0], RIGHT, buff=SMALL_BUFF)
        formule4.add(new_expression)
        
        self.play(FadeIn(new_expression), FadeIn(d))
        self.play(formule4.animate.shift(UP*1.5))