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Quick TrainerCommon Derivatives and Integrals
Recall the standard derivative and integral rules every calculus student needs at their fingertips.
Math33 items4 levelsDifficulty 3/5
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Levels
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1
Basic Derivatives
8 items
2
Basic Integrals
7 items
3
Advanced Derivatives
11 items
4
Advanced Integrals
7 items
All 33 cards
d/dx [c] (constant)
0
d/dx [x^n]
n*x^(n-1)
d/dx [x]
1
d/dx [e^x]
e^x
d/dx [ln x]
1/x
d/dx [sin x]
cos x
d/dx [cos x]
-sin x
d/dx [sqrt(x)]
1/(2 sqrt(x))
∫ 1 dx
x + C
∫ x^n dx (n ≠ -1)
x^(n+1)/(n+1) + C
∫ 1/x dx
ln|x| + C
∫ e^x dx
e^x + C
∫ sin x dx
-cos x + C
∫ cos x dx
sin x + C
∫ sec^2 x dx
tan x + C
d/dx [tan x]
sec^2 x
d/dx [sec x]
sec x tan x
d/dx [csc x]
-csc x cot x
d/dx [cot x]
-csc^2 x
d/dx [a^x]
a^x ln a
d/dx [arcsin x]
1/sqrt(1-x^2)
d/dx [arctan x]
1/(1+x^2)
d/dx [arccos x]
-1/sqrt(1-x^2)
Product rule: d/dx [u·v]
u'v + uv'
Quotient rule: d/dx [u/v]
(u'v - uv')/v^2
Chain rule: d/dx [f(g(x))]
f'(g(x))·g'(x)
∫ a^x dx
a^x/ln a + C
∫ 1/(1+x^2) dx
arctan x + C
∫ 1/sqrt(1-x^2) dx
arcsin x + C
∫ sec x tan x dx
sec x + C
∫ csc^2 x dx
-cot x + C
∫ tan x dx
ln|sec x| + C
∫ ln x dx
x ln x - x + C
