求y=cos²x/2的导数。 y=xcosx2的导数怎么求？
\u6c42y=cos³x \u7684\u5bfc\u51fd\u6570y\u2018=3cos²x*(cosx)'
=3cos²x(-sinx)
=-3sinxcos²x
\u3010\u6570\u5b66\u7684\u5feb\u4e50\u3011\u56e2\u961fwdxf4321\u4e3a\u60a8\u89e3\u7b54\uff01\u795d\u60a8\u5b66\u4e60\u8fdb\u6b65
\u4e0d\u660e\u767d\u53ef\u4ee5\u8ffd\u95ee\uff01
\u6ee1\u610f\u8bf7\u70b9\u51fb\u4e0b\u9762\u7684\u3010\u9009\u4e3a\u6ee1\u610f\u56de\u7b54\u3011\u6309\u94ae\uff0cO(\u2229_\u2229)O\u8c22\u8c22
\u79ef\u6cd5\u5219
(fg)'=f'g+fg'
\u94fe\u5f0f
f(g(x))'=f'(g(x))*g'(x)
\u5148\u6c42cos(x^2)\u7684\u5bfc\u6570
\u663e\u7136\u5bf9\u5e94\u7684
f(x)=cosx
g(x)=x^2
f(g(x))'=f'(g(x))*g'(x)
=-sin(x^2)*2x
\u5bf9\u4e8e\u6574\u4f53\uff0cf(x)=x,g(x)=cos(x^2)
(fg)'=f'g+fg'
=1*cos(x^2)+x*[-sin(x^2)*2x]
=cos(x^2)-sin(x^2)*2x^2
题目是我写的那个吧~
y=cos²(x/2)
y'=-2cos(x/2)sin(x/2)/2
= -0.5sinx
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