calc derivative rules flashcards

d/dx (x^n)

nx^n-1 (power rule)

d/dx[f(g(x))]

f'(g(x))g'(x) (Chain Rule)

d/dx [f(x) g(x)]

f(x) g'(x) + g(x) f'(x) (Product Rule)

d/dx [f(x)/g(x)]

d(g(x) f'(x) - f(x) g'(x)) / (g(x))^2 (Quotient Rule)

d/dx sin x

cos x

d/dx cos x

- sin x

d/dx tan x

sec^2 x

d/dx csc x

-csc(x) cot(x)

d/dx sec x

sec(x) tan(x)

d/dx cotx

-csc^2x

d/dx eˣ

eˣ

d/dx a^x

a^x ln(a)

d/dx lnx

1/x

d/dx loga(x)

1/xlna

d/dx arcsin x

1/√(1-x^2)

d/dx arccos x

-1/√(1-x^2)

d/dx arctan(x)

1/(1+x^2)

if f and g are inverses, then g'(x)

1/f'(g(x))