Ap Calc 2.1 to 2.4

normal derivaitve (limit formula

what are the derivatives that fail to exist and what is like their equations and differentiability based on this(4 graphically and algebrically)

derivatives fail to exist when their limits DNE at a certain point, x, = function not differentiable at that point

1. 1. corner: whatevers in their absolute value solve for x and derivative dne

2. 2. cusp: only not differentiable at x= 0 if equation is x^n where n is between 0 and 1

3. 3. vertical tangent: has a 0 in the denominator (might be same as rule above)

4. 4. discontinouty anywehre its not continous

3 differentiability things (point, interval, differetnai

differentiable and continuity relationship

• differentiabile at x=c has to be continous at x=c

• continous at x=c doesnt always mean differentiable x=c

• not continous = not differentiable at x=c

altenrative form of the derivative

derivative of sine and cosine

normal line is what to the tangent line

perpindicular (slopes that are opposite reciprocals) 4 to -1/4

product rule

first function * derivative of the second + second function * derivative of the first

quotient rule

derivatives of trig functions patterns and what they are

left - right co for everything

derivative of cos (the right) are negative

know the left side and youll know the right side

chain rule (composite)

chain rule/power rule (chain rule always in effect) and when do u stop

** u can be a function (when function inside a power), u stop when u take the derivative of the inner layer

derivatives of natural log + chain rule natural log

derivatives of exponential function +chain rule of exponetial