Find y′ of y=(x−1)(x−4)(x−2)(x−3)
y′=ddx[(x−1)(x−4)(x−2)(x−3)]y′=(x−2)(x−3)ddx[(x−1)(x−4)]−(x−1)(x−4)ddx[(x−2)(x−3)][(x−2)(x−3)]2y′=(x−2)(x−3)[(x−1)ddx(x−4)+(x−4)ddx(x−1)]−(x−1)(x−4)[(x−2)ddx(x−3)+(x−3)ddx(x−2)](x−2)2(x−3)2y′=(x−2)(x−3)[(x−1)(1)+(x−4)(1)]−(x−1)(x−4)[(x−2)(1)+(x−3)(1)](x−2)2(x−3)2y′=(x−2)(x−3)(x−1+x−4)−(x−1)(x−4)(x−2+x−3)(x−2)2(x−3)2y′=(x−2)(x−3)(2x−5)−(x−1)(x−4)(2x−5)(x−2)2(x−3)2y′=(2x−5)[(x−2)(x−3)−(x−1)(x−4)](x−2)2(x−3)2y′=(2x−5)(\cancelx2−\cancel3x−\cancel2x+6−\cancelx2+\cancel4x+\cancelx−4)(x−2)2(x−3)2y′=(2x−5)(2)(x−2)2(x−3)2y′=2(2x−5)(x−2)2(x−3)2
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