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DIFFERENTIATE: x^n
n x ^ (n-1)
DIFFERENTIATE: sin x
cos x
DIFFERENTIATE: cos x
-sin x
DIFFERENTIATE: tan x
sec²(x)
DIFFERENTIATE: cot x
-csc²x
DIFFERENTIATE: sec x
sec x tan x
DIFFERENTIATE: csc x
-csc x cot x
DIFFERENTIATE: ln x
( 1/x ) x’ (if chain rule is necessary)
DIFF: log a (x)
ln (x) / ln (a) == (1/ ln a )(1 /x) (x’)
DIFFERENTIATE: a^u
(a^u) (ln a) (u’)
CHAIN RULE DIFFERENTIATE: f ( g(x) )
f’(g(x)) (g’(x))
INTEGRATE: sin u
-cos u + C
INTEGRATE: cos u
sin u + C
INTEGRATE: sec² u
tan u + C
INTEGRATE: sec u tan u
sec u + C
INTEGRATE: csc u cot u
-csc u + C
INTEGRATE: tan u
-ln |cos u| + C
INTEGRATE: cot u
ln |sin u| + C
INTEGRATE: sec u
ln |sec u + tan u| + C
INTEGRATE: csc u
-ln |csc u + cot u| + C
INTEGRATE: 1/u
ln |u| + C
INTEGRATE: a^u
(a^u)/(ln a)