第1821题：高阶导数
以下高阶导数公式正确的有( ).
A. (sinx)(n)=sin(x+nπ2)(\sin x)^{(n)} =\sin \Big ( x+\dfrac{n \pi}{2} \Big )(sinx)(n)=sin(x+2nπ)
B. (cosx)(n)=cos(x+nπ2)(\cos x)^{(n)} =\cos \Big ( x+\dfrac{n \pi}{2} \Big )(cosx)(n)=cos(x+2nπ)
C. (sinx)(2n)=(−1)nsinx(\sin x) ^{(2n)}=(-1)^n \sin x(sinx)(2n)=(−1)nsinx
D. (sinx)(2n−1)=(−1)n−1sinx(\sin x) ^{(2n-1)}=(-1)^{n-1} \sin x(sinx)(2n−1)=(−1)n−1sinx
E. (uv)′′=u′′v+u′v′+uv′′(uv)''=u''v+u'v'+uv''(uv)′′=u′′v+u′v′+uv′′
F. (uv)′′′=u′′′v(uv)'''=u'''v(uv)′′′=u′′′v +3u′′v′+3u′v′′+uv′′′+3u''v'+3u'v''+uv'''+3u′′v′+3u′v′′+uv′′′
