AP Calc Ch 3

Product Rule

first times the derivative of the second plus the second times the derivative of the first

Quotient Rule

bottom times derivative of the top minus top times derivative of the bottom over bottom squared

When does particle move right?

positive velocity

When does particle speed up?

velocity and acceleration have same sign

When does particle change directions?

velocity changes sign

When is acceleration negative/positive?

when slope is negative/positive

When is the particle moving towards the origin?

position and velocity have opposite signs

When is particle moving away from the origin?

position and velocity have same signs

d/dx(sinx)

cosx

d/dx(cosx)

-sinx

d/dx(tanx)

sec^2x

d/dx(cotx)

-csc^2x

d/dx(secx)

secxtanx

d/dx(cscx)

-cscxcotx