arctan(x)、arccot(x)、arcsin(x)、 arccos(x)各自求导等于多少?

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arctan(x)、arccot(x)、arcsin(x)、 arccos(x)各自求导等于多少?

arctan(x)、arccot(x)、arcsin(x)、 arccos(x)各自求导等于多少?
arctan(x)、arccot(x)、arcsin(x)、 arccos(x)各自求导等于多少?

arctan(x)、arccot(x)、arcsin(x)、 arccos(x)各自求导等于多少?

都换成反函数,再用复合函数求导法。——————————————————————y = arcsinxsiny = xcosy * y' = 1y' = 1/cosy = 1/√(1 - sin²y) = 1/√(1 - x²)——————————————————————y = arccosxcosy = x- siny * y' = 1y' = - 1/siny = - 1/√...

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都换成反函数,再用复合函数求导法。——————————————————————y = arcsinxsiny = xcosy * y' = 1y' = 1/cosy = 1/√(1 - sin²y) = 1/√(1 - x²)——————————————————————y = arccosxcosy = x- siny * y' = 1y' = - 1/siny = - 1/√(1 - cos²y) = - 1/√(1 - x²)——————————————————————y = arctanxtany = xsec²y * y' = 1y' = 1/sec²y = 1/(1 + tan²y) = 1/(1 + x²)——————————————————————y = arccotxcoty = x- csc²y * y' = 1y' = - 1/csc²y = - 1/(1 + cot²y) = - 1/(1 + x²)

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(arctan x)'=1/(1+x^2)
(arccot x)'=(pi/2-(arctan x))'=-1/(1+x^2)
(arcsin x)'=1/根号(1-x^2)
(arccos x)'=-1/根号(1-x^2)