ap calc bc stuff to remember

trig derivatives, exponential derivatives, log derivatives

d/dx sin x

cos x

d/dx cos x

-sin x

d/dx tan x

sec²x

d/dx cot x

-csc²x

d/dx sec x

sec x × tan x

d/dx csc x

-csc x × cot x

d/dx a^x

ln a × a^x

d/dx e^x

e^x

d/dx log_ax

1 / (ln a × x)

d/dx ln x

1 / x

d/dx xⁿ

nx^n-1

derivative of inverse function g(x)

1 /  g’ (g^-1(x))

d/dx sin^-1(g)

g’ / √ 1-g²

d/dx cos^-1(g)

-g’ / √1-g²

d/dx sec^-1(g)

g’ / |g| √g²-1

d/dx csc^-1(g)

-g^’ / |g| √g²-1

d/dx tan^-1(g)

g’ / 1+g²

d/dx cot^-1(g)

-g’ / 1+g²

y = f(g(x)) (chain rule)

f’(g(x))g’(x)

y= f(x)g(x) (product rule)

f’(x)g(x) + f(x)g’(x)

y= f(x) / g(x) (quotient rule)

f’(x)g(x) - f(x)g’(x) / g(x)²

y= f(g(h(x))) (chain inside of a chain)

𝑓′(𝑔(ℎ(𝑥))⋅𝑔′(ℎ(𝑥))⋅ℎ′(𝑥)

d/dx e^g(x)

e^g(x) x g’(x)

d/dx a^g(x)

ln a x a^g(x) x g’(x)

d/dx ln (g(x))

1/ g(x) x g’(x)

d/dx log_a(g(x))

1 / (ln a x g(x)) x g’(x)

g’(x) when f(g(x)) = x

1 / f’ (g(x))

integral of xⁿ

x^n-1/n+1 +c

integral of a^x

a^x / ln a +c

integral of tan x

-ln |cos x| +c

integral of cot x

ln |sin x| +c

integral of sec x

ln |sec x + tan x| + c

integral of csc x

-ln |csc x + cot x| + c

integral of log_ax

x ln x - x / ln a +c