根号怎么求导？望大神解惑 根号下怎么求导
\u6839\u53f7\u4e0b\u600e\u4e48\u6c42\u5bfc\u6839\u53f7\u5c31\u662f\u8868\u793a\u67d0\u6570\u5f002\u5206\u4e4b1\u6b21\u6839\u3002
\u516c\u5f0f\u662f (x^n)'=nx^(n-1)
\u516c\u5f0f\u7684\u610f\u601d\u662fx\u7684n\u6b21\u65b9\u6c42\u5bfc\uff0c\u7b49\u4e8en\u4e58\u4ee5x\u7684n-1\u6b21\u65b9\u3002
\u4f8b\u5982\uff1a
\u221ax = x\u76842\u5206\u4e4b1\u6b21\u65b9 =\uff08x\uff09^\uff081/2\uff09
\u6c42\u5bfc
\uff081/2\uff09 x ^\uff081/2 - 1 \uff09
= \uff081/2\uff09 x ^\uff08 - 1/2 \uff09= 1 / \uff082\u221ax\uff09
\u53c8\u5982\uff1a
y = a\u5f003\u6b21\u65b9\u6c42\u5bfc\uff0c\u3010y = a^(1/3) \u3011
y' = \uff081/3\uff09a^ \uff081/3 - 1 \uff09
\u901a\u5e38\uff0c\u6839\u53f7\u5c31\u662f\u8868\u793a\u67d0\u6570\u5f002\u5206\u4e4b1\u6b21\u6839\u3002
\u4f8b\u5982\uff1a
\u221ax = x\u76842\u5206\u4e4b1\u6b21\u65b9 =\uff08x\uff09^\uff081/2\uff09\u6c42\u5bfc
\uff081/2\uff09 x ^\uff081/2 - 1 \uff09
= \uff081/2\uff09 x ^\uff08 - 1/2 \uff09
= 1 / \uff082\u221ax\uff09
\u53c8\u5982\uff1a
y = a\u5f003\u6b21\u65b9\u6c42\u5bfc\uff0c\u3010y = a^(1/3) \u3011
y' = \uff081/3\uff09a^ \uff081/3 - 1 \uff09
\u5ef6\u4f38\u81f3\u5f00\u4e00\u4e2a\u6570\u7684n\u6b21\u65b9\uff0c\u90fd\u53ef\u4ee5\u628a\u5b83\u5316\u6210\u4e00\u4e2a\u6570\u7684n\u5206\u4e4b1\u3002
\u8fd9\u6837\u5c31\u53ef\u4ee5\u6bd4\u8f83\u8f7b\u677e\u6c42\u5bfc\u3002
\u51fd\u6570 \u88ab\u79f0\u4e3a\u5e42\u6307\u51fd\u6570\uff0c\u5728\u7ecf\u6d4e\u6d3b\u52a8\u4e2d\u4f1a\u5927\u91cf\u6d89\u53ca\u6b64\u7c7b\u51fd\u6570\uff0c\u6ce8\u610f\u5230\u5b83\u5f88\u7279\u522b\u3002\u65e2\u4e0d\u662f\u6307\u6570\u51fd\u6570\u53c8\u4e0d\u662f\u5e42\u51fd\u6570\uff0c\u5b83\u7684\u5e42\u5e95\u548c\u6307\u6570\u4e0a\u90fd\u6709\u81ea\u53d8\u91cfx\uff0c\u6240\u4ee5\u4e0d\u80fd\u7528\u521d\u7b49\u51fd\u6570\u7684\u5fae\u5206\u6cd5\u5904\u7406\u4e86\u3002\u8fd9\u91cc\u4ecb\u7ecd\u4e00\u4e2a\u4e13\u95e8\u89e3\u51b3\u6b64\u7c7b\u51fd\u6570\u7684\u65b9\u6cd5\uff0c\u5bf9\u6570\u6c42\u5bfc\u6cd5\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u5bfc\u6570\u516c\u5f0f\uff1a
1.C'=0(C\u4e3a\u5e38\u6570)\uff1b
2.(Xn)'=nX(n-1) (n\u2208R)\uff1b
3.(sinX)'=cosX\uff1b
4.(cosX)'=-sinX\uff1b
5.(aX)'=aXIna \uff08ln\u4e3a\u81ea\u7136\u5bf9\u6570)\uff1b
6.(logaX)'=\uff081/X)logae=1/(Xlna) (a>0\uff0c\u4e14a\u22601)\uff1b
7.(tanX)'=1/(cosX)2=(secX)2
8.(cotX)'=-1/(sinX)2=-(cscX)2
9.(secX)'=tanX secX\uff1b
10.(cscX)'=-cotX cscX\uff1b
\u53cd\u51fd\u6570\u6c42\u5bfc\u6cd5\u5219\uff1a
\u82e5\u51fd\u6570 \u4e25\u683c\u5355\u8c03\u4e14\u53ef\u5bfc\uff0c\u5219\u5176\u53cd\u51fd\u6570 \u7684\u5bfc\u6570\u5b58\u5728\u4e14 \u3002
\u590d\u5408\u51fd\u6570\u6c42\u5bfc\u6cd5\u5219\uff1a
\u82e5 \u5728\u70b9x\u53ef\u5bfc \u5728\u76f8\u5e94\u7684\u70b9u\u4e5f\u53ef\u5bfc\uff0c\u5219\u5176\u590d\u5408\u51fd\u6570 \u5728\u70b9x\u53ef\u5bfc\u4e14 \u3002
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1---\u6c42\u5bfc
根号的话，就是：
①开平方根，你可以弄成1/2，譬如：
@开3次方，就是1/3，譬如：
诸如此类的，转化一下，后面的形式的话，你应该都会求导的
比如√x求导为1/2√x，那么[√f(x)]'=f'(x)/2√f(x)
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