Question

高数，高阶的导数变化率13谢谢78

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Answer 1

y=x^2sin2x
y^(50)=(x^2sin2x)^(50)
y^(50)=Σ(0,50)C(50,r)(x^2)^(r)*sin2x^(50-r)
=C(50,0)(x^2)*sin2x^(50)+C(50,1)(2x)sin2x^(49)+C(50,2)*2sin2x^(48)
=(x^2)*2^50*sin(2x+50*π/2)+50*(2x)*2*2^49sin(2x+49*π/2)+49*25*2*2^48sin(2x+48*π/2)
=-(x^2)*2^50*sin(2x)+25x*2^52sin(2x+π/2)+49*25*2^49sin(2x)
=-(x^2)*2^50*sin(2x)+25x*2^52cos(2x)+49*25*2^49sin(2x)