AP Calc A/B Formulas

Not all of them are here, but hopefully this helps a little bit!

d/dx(sinx)

cosx

d/dx(cosx)

-sinx

d/dx(tanx)

sec²x

d/dx(secx)

secxtanx

d/dx(cscx)

-cscxcotx

d/dx(cotx)

-csc²x

d/dx(arcsinx)

1/rad(1-x²)

d/dx(arccosx)

-1/rad(1-x²)

d/dx(arctanx)

1/(1+x²)

d/dx(a^x)

a^xln(a)

d/dx(e^x)

e^x

d/dx(lnx)

1/x

d/dx(|lnx|)

1/x

d/dx(loga(x))

1/xlna

Mean Value Theorem

If f(x) is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there is a number where a<c<b where IROC=AROC.

Pythagorean Identities

sin²x+cos²x=1

tan²x+1=sec²x

1+cot²x=csc²x

ln1=

0

d/dx(ln(a^n))=

nln(a)

ln(ab)=

lna+lnb

ln(a/b)

lna-lnb

Rolle’s Theorem

If f is continuous on [a,b] and differentiable on (a,b). If f(a)=f(b), then at least one number c in (a,b) where f’©=0. If true, there is at least one number between a and b where the tangent line is horizontal.

d/dx[arccscu]=

-u’/|u|rad(u²-1)

d/dx[arcsecu]=

u’/|u|rad(u²-1)

d/dx[arccotu]=

-u’/(1+u²)

integral of sinu du=

-cosu+C

integral of cosu du=

sinu+C

integral of tanu du=

-ln|cosu|+C

integral of cscu du=

-ln|cscu+cotu|+C

integral of secu du=

ln|secu+tanu|+C

integral of cotu du=

ln|sinu|+C

integral of 1/u du=

ln|u|+C

integral of a^u du=

a^u/(lna) +C

integral of 1/rad(a²-u²) du=

arcsin(u/a)+C

integral of 1/urad(u²-a²) du=

1/a arcsec(|u|/a) +C

integral of 1/a²+u² du=

1/a arctan(u/a)+C

cos2x=2cos²x-1 Rewritten

cos²x=(1+cos2x)/2

cos2x=1-2sin²x Rewritten

sin²x=(1-cos2x)/2

sin2x Rewritten

2sinxcosx

lim as theta approaches 0 of sintheta/theta =

1

lim as theta approaches 0 of (1-costheta)/theta=

0