Log/Exponent Properties: ln(1) = 0 ln(e) = 1 ln(an) = n*ln(a) ln(ab) = ln(a) + ln(b)

baba lnlnln =

Exponent Properties: ea * eb = ea+b (ea)b = eab e0 = 1

Log Differentiation steps: 1) Take ln of both sides. 2) Expand right side. 3) Find derivative 4) Solve for dy/dx Evaluate derivative of inverse: (find !! !() 1.Set f(x) = a and solve for x (guess and check) 2. Find f (x) 3. Plug in x value from step #1 into f (x). 4. Flip value.

Log Derivatives: Exponential Derivatives ddxln | u |= u '

u

ddxeu = eu u '

uu

au

dxd

a'*

ln1log =

ddxau = lnaau *u '

Trig Derivatives: d

dxsinu = cosu*u '

ddxtanu = sec2 u*u '

ddxsecu = secu tanu*u '

ddxcosu = sinu*u '

ddxcotu = csc2 u*u '

ddxcscu = cscucotu*u '

Inverse Trig Derivatives: ddxarcsinu = u '

1u2 ddxarctanu = u '

1+u2 ddxarcsecu = u '

u u2 1

ddxarccosu = u '

1u2 ddxarccotu = u '

1+u2

ddxarccscu = u '

u u2 1

Integral Formulas: Power Rule:

un du = un+1

n+1+C

Log Rule: 1udu = ln | u |+C

Exponential Rule: (Base e) dueu = e

u + C

Exponential Rule (base other than e)

au du = au

lna+C

*Note: lna is a constant*

Trig Integrals: sinudu = cosu+C cosudu = sinu+C sec2 udu = tanu+C secu tanudu = secu+C csc2 udu = cotu+C cscucotudu = cscu+C

C + |cosu|-lntan = udu Cuudu += sinlncot

udusec = ln|sec u + tan u| + C

uducsc = -ln|csc u + cot u| + C

Inverse Trig Integrals:

+=

Cau

uadu arcsin

22 +=+ Ca

uaua

du arctan122

+=

Cau

aauudu ||secarc1

22

!"#! ! = and log! ! =

log! = ln ln

Interest Formulas

= !1 +!(!")

A = Pert