Calculus

Question 1

Definition of Derivative

Answer 1

lim h->0 [F(x+h) - F(x)] / h

Question 2

Product Rule

Answer 2

y = f(x)g(x)h(x) y’ = f’(x)g(x)h(x) + f(x)g’(x)h(x) + f(x)g(x)h’(x)

Question 3

Quotient Rule

Answer 3

[(bottom)(top’) - (top)(bottom’)] / (bottom)²

Question 4

Derivative y = sin(x)

Answer 4

y’ = cos(x)

Question 5

Derivative y = cos(x)

Answer 5

y’ = -sin(x)

Question 6

Derivative y = tan(x)

Answer 6

y’ = sec²(x)

Question 7

Derivative y = sec(x)

Answer 7

y’ = sec(x)*tan(x)

Question 8

Derivative y = cot(x)

Answer 8

y’ = -csc²(x)

Question 9

Derivative y = csc(x)

Answer 9

y’ = -csc(x)*cot(x)

Question 10

cos30º =

Answer 10

√3 / 2

Question 11

tan30º =

Answer 11

√3 / 3

Question 12

sin30º =

Answer 12

1/2

Question 13

Derivative y = arcsin(x)

Answer 13

y’ = x¹ / (√1-x²)

Question 14

Derivative y = arccos(x)

Answer 14

y’ = -x¹ / (√1-x²)

Question 15

Derivative y = arctan(x)

Answer 15

y’ = x¹ / 1+x²

Question 16

sinh(x) =

Answer 16

(e ͯ - eˉ ͯ) / 2

Question 17

cosh(x) =

Answer 17

(e ͯ + eˉ ͯ) / 2

Question 18

cos(A ± B) =

Answer 18

cosAcosB -+ sinAsinB =

Question 19

sin(A ± B) =

Answer 19

sinAcoB -+ sinBcosA =

Question 20

cos²θ + sin²θ =

Answer 20

1 =

Question 21

sec²θ =

Answer 21

tan²θ + 1 =

Question 22

csc²θ =

Answer 22

cot²θ + 1 =

Question 23

Derivative sinh(x)

Answer 23

sinh(x)(x’)

Question 24

Derivative tanh(x)

Answer 24

sech²(x)(x’)

Question 25

Derivative sech(x)

Answer 25

-sech(x)*tanh(x)(x')

Question 26

Derivative cosh(x)

Answer 26

sinh(x)(x')

Question 27

Derivative csch(x)

Answer 27

-csc(c)*-coth(x)(x')

Question 28

Derivative coth(x)

Answer 28

-csch²(x)(x')

Question 29

Position vs. Velocity vs. Acceleration

Answer 29

s, s' = ∆s/∆t, s'' = ∆v/∆t = -32ft/sec

Question 30

Average Value

Answer 30

1/b-a ∫ba f(x)dx

Question 31

Log(a*b)

Answer 31

logA + logB

Question 32

Log(a/b)

Answer 32

logA - logB

Question 33

Sin2x =

Answer 33

2(cosx)(sinx)

Question 34

Vertical Asymptotes

Answer 34

Set base to zero... F(x)

Question 34

Logb ͯ =

Answer 34

xLogb