cos2x怎么求导 cos2x的导数是多少、?
cos2x\u7684\u5bfc\u6570cos2x\u7684\u5bfc\u6570\u4e3a-2sin2x\u3002\u5177\u4f53\u89e3\u9898\u8fc7\u7a0b\u5982\u4e0b\uff1a
\u89e3\uff1a(cos2x)'
=-sin2x*(2x)'
=-2sin2x
\u6269\u5c55\u8d44\u6599\uff1a
1\u3001\u5bfc\u6570\u7684\u56db\u5219\u8fd0\u7b97\u89c4\u5219
\uff081\uff09\uff08f(x)\u00b1g(x)\uff09'=f'(x)\u00b1g'(x)
\u4f8b\uff1a\uff08x^3-cosx\uff09'=(x^3)'-(cosx)'=3*x^2+sinx
\uff082\uff09\uff08f(x)*g(x)\uff09'=f'(x)*g(x)+f(x)*g'(x)
\u4f8b\uff1a\uff08x*cosx\uff09'=(x)'*cosx+x*(cosx)'=cosx-x*sinx
\uff083\uff09\uff08f(x)/g(x)\uff09'=\uff08f'(x)*g(x)-f(x)*g'(x)\uff09/(g(x))^2
\u4f8b\uff1a\uff08sinx/x\uff09'=\uff08(sinx)'*x-sinx*(x)'\uff09/x^2=\uff08x*cosx-sinx\uff09/x^2
2\u3001\u7b26\u5408\u51fd\u6570\u7684\u5bfc\u6570\u6c42\u6cd5
\u590d\u5408\u51fd\u6570\u5bf9\u81ea\u53d8\u91cf\u7684\u5bfc\u6570\uff0c\u7b49\u4e8e\u5df2\u77e5\u51fd\u6570\u5bf9\u4e2d\u95f4\u53d8\u91cf\u7684\u5bfc\u6570\uff0c\u4e58\u4ee5\u4e2d\u95f4\u53d8\u91cf\u5bf9\u81ea\u53d8\u91cf\u7684\u5bfc\u6570\u3002
\u5373\u5bf9\u4e8ey=f(t)\uff0ct=g(x)\uff0c\u5219y'\u516c\u5f0f\u8868\u793a\u4e3a\uff1ay'=\uff08f(t)\uff09'*\uff08g(x)\uff09'
\u4f8b\uff1ay=sin\uff08cosx\uff09\uff0c\u5219y'=cos(cosx)*(-sinx)=-sinx*cos(cosx)
3\u3001\u5e38\u7528\u7684\u5bfc\u6570\u516c\u5f0f
\uff08lnx\uff09'=1/x\u3001\uff08e^x\uff09'=e^x\u3001\uff08C\uff09'=0\uff08C\u4e3a\u5e38\u6570\uff09\u3001\uff08sinx\uff09'=cosx\u3001\uff08cosx\uff09'=-sinx
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u641c\u72d7\u767e\u79d1-\u5bfc\u6570
-2sin2x
\u8bbey=2x,\u5219\u6709cosy\u7684\u5bfc\u6570=-siny*y\u7684\u5bfc\u6570,\u5373cos2x=-sin2x*2=-2sin2x
（cos2x)'=-sin2x·(2x)'=-2sin2x
y=cos2x是由y=cosu，u=2x复合而成的，因此
y′=y′u·u′x=-sinu·2=-2sin2x
复合函数求导，外导乘内导
2x=u
(cos2x)的导=cos u的导×u的导
=-sin2x×2
=-2sin2x
Chain Rule:
(cos2x)' = -sin2x (2x)' = -2sin2x
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