Unit 2

Question 1

derivative of cosx

Answer 1

-sinx

Question 2

derivative of sinx

Answer 2

cosx

Question 3

derivative of a to the x

(a^x)

Answer 3

a to the x times natural log of a

(a^x) * lna

Question 4

derivative of e to the x

(e^x)

Answer 4

e to the x

(e^x)

Question 5

derivative of log (base a) of x

log_a (x)

Answer 5

(1 / xlna)

Question 6

derivative of log (base e) of x

log_e (x)

Answer 6

1/x

Question 7

product rule

f*g

Answer 7

(f’(x)g(x)) + (f(x)g’(x))

Question 8

quotient rule

f / g

Answer 8

(low d-high) minus (high d-low) all over lowlow

( (g(x) * f’(x)) - (f(x) * g’(x)) ) / (g(x))^2

Question 9

dv tanx

Answer 9

sec^2 x

Question 10

dv cotx

Answer 10

-csc^2 x

Question 11

dv secx

Answer 11

secx * tanx

Question 12

dv cscx

Answer 12

-cscx * cotx

Question 13

normal line?

Answer 13

same as tangent BUT it has the NEGATIVE and reciprocal version of the slope

ex.
tangent: y-1= 2(x-1)
normal: y-1 = -(1/2)(x-1)

Question 14

point slope form

Answer 14

y-y1 = m (x-x1)

Question 15

derivative doesn’t exist if

Answer 15

1. discontinuity (like a hole, jump, or asymptotes)
2. corner or cusp
3. vertical tangent

NOT a horizontal tangent