Mathematics Integration and Derivative Basics

d/dx [C]

0

d/dx [kx]

k

d/dx [kf(x)]

kf'(x)

d/dx [f(x) ± g(x)]

f'(x) ± g'(x)

d/dx [x^n]

nx^(n-1)

d/dx [sin x]

cos x

d/dx [cos x]

-sin x

d/dx [tan x]

sec^2 x

d/dx [sec x]

sec x tan x

d/dx [cot x]

-csc^2 x

d/dx [csc x]

-csc x cot x

∫ 0 dx

C

∫ k dx

kx + C

∫ k f(x) dx

k ∫ f(x) dx

∫ [f(x) ± g(x)] dx

∫ f(x) dx ± ∫ g(x) dx

∫ x^n dx

x^(n+1)/(n+1) + C, n ≠ -1

∫ cos x dx

sin x + C

∫ sin x dx

-cos x + C

∫ sec^2 x dx

tan x + C

∫ sec x tan x dx

sec x + C

∫ csc^2 x dx

-cot x + C

∫ csc x cot x dx

-csc x + C

d/dx [ln|x|]

1/x

∫ 1/x dx

ln|x| + C

d/dx [e^x]

e^x

∫ e^x dx

e^x + C

∫ b^x dx

b^x / ln(b) + C