极坐标方程所确定的函数导数 求参数方程所确定的函数导数 x=1-t² y=t-...
\u9ad8\u7b49\u6570\u5b66\u95ee\u9898\uff0c\u6c42\u6781\u5750\u6807\u65b9\u7a0b\u8868\u793a\u7684\u51fd\u6570\u7684\u5bfc\u6570d\u03b8/da = (seca)^2-1 = (tana)^2,
d\u03c1/da = Rsecatana
d\u03c1/d\u03b8 = (d\u03c1/da)/(d\u03b8/da)
= Rsecatana/ (tana)^2
= Rseca/tana = Rcsca
\u5bfc\u6570\u4e3a\uff1a\uff083t²-1\uff09/\uff082t\uff09\u3002
\u89e3\u7b54\u8fc7\u7a0b\u5982\u4e0b\uff1a
\u6269\u5c55\u8d44\u6599\uff1a
\u4e00\u4e9b\u5e38\u7528\u7684\u53c2\u6570\u65b9\u7a0b\uff1a
1.\u5706\u7684\u53c2\u6570\u65b9\u7a0b x=a+r cos\u03b8 y=b+r sin\u03b8\uff08\u03b8\u2208 [0\uff0c2\u03c0) \uff09 (a,b) \u4e3a\u5706\u5fc3\u5750\u6807\uff0cr \u4e3a\u5706\u534a\u5f84\uff0c\u03b8 \u4e3a\u53c2\u6570\uff0c(x,y) \u4e3a\u7ecf\u8fc7\u70b9\u7684\u5750\u6807\u3002
2.\u692d\u5706\u7684\u53c2\u6570\u65b9\u7a0b x=a cos\u03b8\u3000 y=b sin\u03b8\uff08\u03b8\u2208[0\uff0c2\u03c0\uff09\uff09 a\u4e3a\u957f\u534a\u8f74\u957f b\u4e3a\u77ed\u534a\u8f74\u957f \u03b8\u4e3a\u53c2\u6570\u3002
3.\u53cc\u66f2\u7ebf\u7684\u53c2\u6570\u65b9\u7a0b x=a sec\u03b8 \uff08\u6b63\u5272\uff09 y=b tan\u03b8 a\u4e3a\u5b9e\u534a\u8f74\u957f b\u4e3a\u865a\u534a\u8f74\u957f \u03b8\u4e3a\u53c2\u6570\u3002
4.\u629b\u7269\u7ebf\u7684\u53c2\u6570\u65b9\u7a0b x=2pt^2 y=2pt p\u8868\u793a\u7126\u70b9\u5230\u51c6\u7ebf\u7684\u8ddd\u79bb t\u4e3a\u53c2\u6570\u3002
\u5e38\u7528\u5bfc\u6570\u516c\u5f0f\uff1a
1.y=c(c\u4e3a\u5e38\u6570) y'=0
2.y=x^n y'=nx^(n-1)
3.y=a^x y'=a^xlna\uff0cy=e^x y'=e^x
4.y=logax y'=logae/x\uff0cy=lnx y'=1/x
5.y=sinx y'=cosx
6.y=cosx y'=-sinx
7.y=tanx y'=1/cos^2x
8.y=cotx y'=-1/sin^2x
9.y=arcsinx y'=1/\u221a1-x^2
10.y=arccosx y'=-1/\u221a1-x^2
11.y=arctanx y'=1/1+x^2
nx²
嗯
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