Unit 4

Question 1

d/dx(cu)

Answer 1

cu’

Question 2

d/dx(u +-v)

Answer 2

u’ +- v’

Question 3

d/dx(uv)

Answer 3

uv’+v’u

Question 4

d/dx(u/v)

Answer 4

(vu’-uv’)/v^2

Question 5

d/dx(c)

Answer 5

0

Question 6

d/dx(u^n)

Answer 6

n*u^(n-1)u’

Question 7

d/dx(x)

Answer 7

1

Question 8

d/dx(abs(u))

Answer 8

(u/abs(u))*u’ when u != 0

Question 9

d/dx(lnu)

Answer 9

u’/u

Question 10

d/dx(e^u)

Answer 10

(e^u)*(u’)

Question 11

d/dx(log base a of u)

Answer 11

u’/(lna * u)

Question 12

d/dx(a^u)

Answer 12

ln(a)(a^u)u’

Question 13

d/dx(sinx)

Answer 13

cosx*x’

Question 14

d/dx(cosx)

Answer 14

-(sinx)*u’

Question 15

d/dx(tanx)

Answer 15

sec^2(x)*x’

Question 16

d/dx(cotx)

Answer 16

-(csc^2(x))*x’

Question 17

d/dx(secx)

Answer 17

secxtanxu’

Question 18

d/dx(csc(x))

Answer 18

-csc(x)cot(x)x’

Question 19

d/dx(arcsin(x))

Answer 19

x’/sqrt(1-x^2)

Question 20

d/dx(arccos(x))

Answer 20

-x’/sqrt(1-x^2)

Question 21

d/dx(arctanx)

Answer 21

x’/1+x^2

Question 22

d/dx(arccot(x))

Answer 22

-x’/1+x^2

Question 23

d/dx(arcsec(x))

Answer 23

x’/abs(x)*sqrt(x^2-1)

Question 24

d/dx(arccsc(x))

Answer 24

x’/abs(x)*sqrt(x^2-1)

Question 25

int(k*f(u)du)

Answer 25

k*int(f(u)du

Question 26

int(f(x)+g(x)dx)

Answer 26

int(f(x)dx)+int(g(x)dx)

Question 27

int(du)

Answer 27

u + C

Question 28

int(du/u)

Answer 28

ln(abs(u)) + C

Question 29

int(u^n)du

Answer 29

((u^(n+1))/n+1) + C

Question 30

int(a^u(du))

Answer 30

((a^u)/ln(a))+C

Question 31

int(sinu)du

Answer 31

-cos(u)+C

Question 32

int(cos(u)du)

Answer 32

sinu + C

Question 33

int(tan(u)du)

Answer 33

-ln(abs(cosu)) + C

Question 34

int(cotu)(du)

Answer 34

ln(abs(sinu)) + C

Question 35

int(sec(u)du)

Answer 35

ln(abs(secu + tanu)) + C

Question 36

int(csc(u)du)

Answer 36

-ln(abs(cscu+cotu))+C

Question 37

int(sec^2u du)

Answer 37

tanu + C

Question 38

int(csc^2x)dx

Answer 38

-cotx+C

Question 39

int(secutanudu)

Answer 39

secu + C

Question 40

int(cscx+cotx)dx

Answer 40

-csc(x) + C

Question 41

int(du/(sqrt(a^2 - u^2)))

Answer 41

arcsin(u/a) + C

Question 42

int(du/(a^2+u^2))

Answer 42

(1/a) * arctan(u/a) + C

Question 43

int(du/(u * sqrt(u^2 - a^2)))

Answer 43

(1/a)*arcsec(abs(u)/a) + C