y=arcsinX、arccosX、arctanX、arccotX的导数. 反三角函数的导数求法?如arcsinx arccosx ar...
y=arcsinX\u3001arccosX\u3001arctanX\u3001arccotX\u7684\u5bfc\u6570. \u5982\u9898\u90fd\u6362\u6210\u53cd\u51fd\u6570,\u518d\u7528\u590d\u5408\u51fd\u6570\u6c42\u5bfc\u6cd5.
\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014
y = arcsinx
siny = x
cosy * y' = 1
y' = 1/cosy = 1/\u221a(1 - sin²y) = 1/\u221a(1 - x²)
\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014
y = arccosx
cosy = x
- siny * y' = 1
y' = - 1/siny = - 1/\u221a(1 - cos²y) = - 1/\u221a(1 - x²)
\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014
y = arctanx
tany = x
sec²y * y' = 1
y' = 1/sec²y = 1/(1 + tan²y) = 1/(1 + x²)
\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014
y = arccotx
coty = x
- csc²y * y' = 1
y' = - 1/csc²y = - 1/(1 + cot²y) = - 1/(1 + x²)
\u53cd\u51fd\u6570\u6c42\u5bfc\u65b9\u6cd5:\u82e5F(X),G(X)\u4e92\u4e3a\u53cd\u51fd\u6570,\u5219:
F'(X)*G'(X)=1E.G.:y=arcsinx
x=siny
y'*x'=1
(arcsinx)'*(siny)'=1
y'=1/(siny)'=1/(cosy)=1/\u6839\u53f7(1-sin^2y)=1/\u6839\u53f7(1-x^2)\u5176\u4f59\u4f9d\u6b64\u7c7b\u63a8
Y'= - 1/(√1-X²)
Y'= 1/(1+X²)
Y'.= - 1/(1+X²)
答题不易
祝你学习进步
望采纳 谢谢
y'=1/根号(1-x的平方)、
y'=-1/根号(1-x的平方)、
y'=1/(1+x的平方)、
y'=-1/(1+x的平方)、
都换成反函数，再用复合函数求导法。
——————————————————————
y = arcsinx
siny = x
cosy * y' = 1
y' = 1/cosy = 1/√(1 - sin²y) = 1/√(1 - x²)
——————————————————————
y = arccosx
cosy = x
- siny * y' = 1
y' = - 1/siny = - 1/√(1 - cos²y) = - 1/√(1 - x²)
——————————————————————
y = arctanx
tany = x
sec²y * y' = 1
y' = 1/sec²y = 1/(1 + tan²y) = 1/(1 + x²)
——————————————————————
y = arccotx
coty = x
- csc²y * y' = 1
y' = - 1/csc²y = - 1/(1 + cot²y) = - 1/(1 + x²)
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