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d 2
tan x = sec x
dx

d
csc x = − csc x cot x
dx

d
sec x = sec x tan x
dx

d
2
cot x = − csc x
dx
d 1 π π
arcsin x = √ , − ≤ arcsin x ≤
dx 1 − x 2 2 2

d 1
arccos x = −√ , 0 ≤ arccos x ≤ π
dx 1 − x 2

d 1 π π
arctan x = , − ≤ arctan x ≤
dx 1 + x 2 2 2

d
sinh x = cosh x
dx

d
cosh x = sinh x
dx

d 2
tanh x = sech x
dx

d
csch x = − csch x coth x
dx

d
sech x = − sech x tanh x
dx
d 2
coth x = − csch x
dx

d 1
arcsinh x = √
dx x + 1
2
d 1
arccosh x = √ , x > 1, arccosh x > 0
dx x − 1
2
d 1
2
arctanh x = , x < 1
dx 1 − x 2

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