大学导数公式表有哪些? 常见的导数公式有哪些?
\u5927\u5b66\u5bfc\u6570\u516c\u5f0f\u8868
\u5bfc\u6570\u7684\u5b9a\u4e49\uff1a
\u8bbe\u51fd\u6570y=f(x)\u5728\u70b9x0\u7684\u67d0\u4e2a\u90bb\u57df\u5185\u6709\u5b9a\u4e49\uff0c\u5f53\u81ea\u53d8\u91cfx\u5728x0\u5904\u6709\u589e\u91cf\u0394x\uff0c(x0+\u0394x)\u4e5f\u5728\u8be5\u90bb\u57df\u5185\u65f6\uff0c\u76f8\u5e94\u5730\u51fd\u6570\u53d6\u5f97\u589e\u91cf\u0394y=f(x0+\u0394x)-f(x0)\uff1b\u5982\u679c\u0394y\u4e0e\u0394x\u4e4b\u6bd4\u5f53\u0394x\u21920\u65f6\u6781\u9650\u5b58\u5728\uff0c\u5219\u79f0\u51fd\u6570y=f(x)\u5728\u70b9x0\u5904\u53ef\u5bfc\uff0c\u5e76\u79f0\u8fd9\u4e2a\u6781\u9650\u4e3a\u51fd\u6570y=f(x)\u5728\u70b9x0\u5904\u7684\u5bfc\u6570\u8bb0\u4f5c\u2460 \u2461 \uff1b\u2462 \u5373\uff1a
\u9700\u8981\u6307\u51fa\u7684\u662f\uff1a
\u4e24\u8005\u5728\u6570\u5b66\u4e0a\u662f\u7b49\u4ef7\u7684\u3002
常用导数公式表如下:
c'=0(c为常数)
(x^a)'=ax^(a-1),a为常数且a≠0
(a^x)'=a^xlna
(e^x)'=e^x
(logax)'=1/(xlna),a>0且 a≠1
(lnx)'=1/x
(sinx)'=cosx
(cosx)'=-sinx
(tanx)'=(secx)^2
(secx)'=secxtanx
(cotx)'=-(cscx)^2
(cscx)'=-csxcotx
(arcsinx)'=1/√(1-x^2)
(arccosx)'=-1/√(1-x^2)
(arctanx)'=1/(1+x^2)
(arccotx)'=-1/(1+x^2)
(shx)'=chx
(chx)'=shx
d(Cu)=Cdud(u+-v)=du+-dvd(uv)=vdu+udvd(u/v)=(vdu-udv)/v^2
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