Question

什么的导数是(sinx)的3次方

急啊

Answer 1

∫（sinx)^3dx=-∫（sinx)^2dcosx
=-∫（1-cosx^2)dcosx
=1/3(cosx^3)-cosx+C C为任意常数
即1/3(cosx^3)-cosx+C的导数是(sinx)的3次方

Answer 2

y=sin³x
=sinx(1-cos2x)/2
=[(sinx)/2]-[(sinxcos2x)/2]
=[(sinx)/2]-[(sin3x-sinx)/4]
=(3sinx-sin3x)/4
y^(n)=[3sin(x+nπ/2)-3^n*sin(3x+nπ/2)]/4