f(x)=x*sin2x 则f(0)的五阶导数答案多少?

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f(x)=x*sin2x 则f(0)的五阶导数答案多少?
f(x)=x*sin2x 则f(0)的五阶导数答案多少?

f(x)=x*sin2x 则f(0)的五阶导数答案多少?
f(0)是一个数值而不是函数.正确问法应该是f(x)五阶导数在0点的值.
f(x)=x * sin2x
f'(x)=sin2x+2xcos2x
f''(x)=2cos2x+(2cos2x-4xsin2x)=4cos2x-4xsin2x
f^(3)(x)=-8sin2x-4(sin2x+2xcos2x)=-12sin2x-8xcos2x
f^(4)(x)=-24cos2x-8(cos2x-2xsin2x)=-32cos2x+16xsin2x
f^(5)(x)=64sin2x+16(sin2x+2xcos2x)=80sin2x+32xcos2x
f^(5)(0)=0

f′(x)=sin2x+2xcos2x
f″(x)=2cos2x+2cos2x-4xsin2x
=4cos2x-4xsin2x
f^3（x）=-8sin2x-4sin2x-8xcos2x=-12sin2x-8xcos2x
f^4(x)=-24sin2x-8cos2x+16xsin2x=(16x-24)sin2x-8cos2x
f^5(x)=16sin2x+2(16x-24)cos2x+16sin2x=32sin2x+16(2x-3)cos2x
f^5(0)=32sin0+16cos0=16

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