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Math
Calculus
calc 2
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Match
Terms in this set (24)
...
...
lim cf(x)
c ⋅ lim f(x)
c is constant
lim [f(x) ± g(x)]
lim f(x) ± lim g(x)
lim [f(x) ⋅ g(x)]
lim f(x) ⋅ lim g(x)
lim [f(x) / g(x)]
lim f(x) / lim g(x)
as long as lim g(x)≠0
d
--- (uv) =
dx
u'v + uv'
(product rule)
d f(x)
--- ⋅ ---- =
dx g(x)
g(x) ⋅ f'(x) - f(x) ⋅ g'(x)
-----------------------
[g(x)]^2
(quotient rule)
d
--- (f(g(x))
dx
f'(g(x)) ⋅ g'(x)
(chain rule)
d
--- (sin x) =
dx
cos x
d
--- (cos x) =
dx
-sin x
d
--- (tan x) =
dx
sec^2 x
d
--- (sec x) =
dx
sec x ⋅ tan x
d
--- (cot x) =
dx
-csc^2 x
d
--- (csc x) =
dx
-csc x ⋅ cot x
d
--- (𝑒ˣ) =
dx
𝑒ˣ
d
--- (aˣ) =
dx
aˣ ⋅ ln a
d
--- (ln x) =
dx
1/x
d
--- (log
subscript a
x) =
dx
1
-----
x ln a
d
--- (arcsin x) =
dx
1
------
√1-x²
d
--- (arccos x) =
dx
1
(-) ------
√1-x²
d
--- (arcsec x) =
dx
1
----------
|x| ⋅√1-x²
d
--- (arccsc x) =
dx
1
(-) ----------
|x| ⋅√1-x²
d
--- (arctan x) =
dx
1
------
1 + x²
d
--- (arccot x) =
dx
1
(-) ------
1 + x²
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