Calculus Midterm

Question 1

d/dx (cosu)

Answer 1

-(sinu) u’

Question 2

d/dx (cos (kx))

Answer 2

-ksin(kx)

Question 3

d/dx (tanx)

Answer 3

sec^2(x)

Question 4

d/dx (tanu)

Answer 4

(sec^2u) u’

Question 5

d/dx (cot (x)

Answer 5

-csc^2 x

Question 6

d/dx (cotu)

Answer 6

-(csc^2u)u’

Question 7

d/dx (sin(x))

Answer 7

cosx

Question 8

d/dx (sin(u))

Answer 8

(cosu)u’

Question 9

d/dx (sin(kx))

Answer 9

kcos(kx)

Question 10

d/dx (cosx)

Answer 10

-sinx

Question 11

d/dx (secx)

Answer 11

secxtanx

Question 12

d/dx (secu)

Answer 12

(secutanu) u’

Question 13

d/dx (cscx)

Answer 13

-cscxcotx

Question 14

d/dx (cscu)

Answer 14

-(cscucotu)u’

Question 15

Factor theorem

Answer 15

If P(x) is a polynomial and P(a)=0 then x-a is a factor of P(x)

Question 16

a/b - c/d

Answer 16

(ad-bc)/bd

Question 17

When direct substitution in a limit results in a nonzero number/zero

Answer 17

limit is either +infinity or -infinity or does not exist.

Question 18

sin(0)

Answer 18

0

Question 19

cos (0)

Answer 19

1

Question 20

sin (pi/2)

Answer 20

1

Question 21

Power Rule

Answer 21

d/dx x^n = nx^n-1

Question 22

Definition of a derivative

Answer 22

lim h->0 f(x+h)-f(x)/h

Question 23

Derivative of a sum

Answer 23

(f + g)’ = f’ + g’

Question 24

Chain rule

Answer 24

d/dx f(g(x)) = f’(g(x)) g’(x)

Question 25

Exponential Derivative

Answer 25

d/dx (e^x) = e^x)

Question 26

Exponential derivative chain rule

Answer 26

d/dx (e^u) = (e^u)u’

Question 27

Exponential derivative special case

Answer 27

d/dx e^kx = ke^kx

Question 28

Log Derivative

Answer 28

d/dx ln(x) = 1/x

Question 29

log derivative chain rule form

Answer 29

d/dx ln(u) = u’/u

Question 30

product rule

Answer 30

d/dx (fg) = f’g + fg’

Question 31

ln (1)

Answer 31

0

Question 32

ln(e)

Answer 32

0