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 𝑓!! !(𝑎)    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 = lna∗au *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 '

1−u2  ddxarctanu = u '

1+u2  ddxarcsecu = u '

u u2 −1  

ddxarccosu = − u '

1−u2  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 =  eu  +  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                        ∫ +=

+C

au

auadu arctan1

22                  

∫ +=−

Cau

aauudu ||secarc1

22  

𝑎!"#! ! = 𝑥  and  log! 𝑎! = 𝑥  

log! 𝑥 =  ln 𝑥ln𝑎

 

Interest  Formulas  

𝐴 = 𝑃 !1 +𝑟𝑛!(!")

 

A  =  Pert