跪求有关双曲函数的各种求导公式啊 !!!
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发布时间：2022-04-24 18:55
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时间：2023-07-09 16:23
shx = (e^x - e^(-x)/2, (shx) ' =chx
chx = (e^x + e^(-x)/2, (chx) ' =shx
thx = shx / chx, (thx) ' = 1/(chx)^2
arcsinh x = ln[ x+ (x^2+1)^(1/2) ] , (arcsinh x) ' = 1/ (x^2+1)^(1/2)
arccosh x = ln[ x+ (x^2-1)^(1/2) ] , (arccosh x) ' = 1/ (x^2-1)^(1/2)
arctanh x =(1/2) [ ln(1+x)/(1-x) ], (arctanh x) ' = 1/(1-x^2)
......追问那 csch(x), sech(x), coth(x), arccot(x), arccsch(x), arcseh(x) 的求导呢？？？求大神指点啊
追答coth(x) ' = - (csch x )^2
sech(x) ' = - sechx tanhx
csch(x) ' = - cschx cothx
arccoth(x) ' = 1/(1-x^2)
arcseh(x) ' = -1/[ x √(1-x^2) ]
arccsch(x) ' = -1 / √ [ x^2 (1+x^2) ]
