Derivatives

Question 1

d/dx (cu)

Answer 1

cu’

Question 2

d/dx (x +- v)

Answer 2

u’ +- v’

Question 3

d/dx (uv)

Answer 3

uv’ + vu’

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

(nu^n-1)u’

Question 7

d/dx (x)

Answer 7

1

Question 8

d/dx (|u|)

Answer 8

(u/|u|) u’, u no equal 0

Question 9

d/dx (ln(u))

Answer 9

u’/u

Question 10

d/dx (e^u)

Answer 10

e^u(u’)

Question 11

d/dx (log_a(u))

Answer 11

u’/(lna)(u)

Question 12

d/dx (a^u)

Answer 12

(lna)(a^u)u’

Question 13

d/dx (sin(u))

Answer 13

(cos(u))u’

Question 14

d/dx (cos(u))

Answer 14

-(sin(u))u’

Question 15

d/dx (tan(u))

Answer 15

(sec^2(u))u’

Question 16

d/dx (cot (u))

Answer 16

-(csc^2(u))u’

Question 17

d/dx (sec(u))

Answer 17

(sec(u))(tan(u))u’

Question 18

d/dx (csc(u))

Answer 18

-(csc(u)cot(u))u’

Question 19

d/dx (arcsin(u))

Answer 19

u’ / root(1-u^2)

Question 20

d/dx (arccos(u))

Answer 20

-u’ / root(1-u^2)

Question 21

d/dx (arctan(u))

Answer 21

u’ / 1 + u^2

Question 22

d/dx (arccot(u))

Answer 22

-u’ / 1+u^2

Question 23

d/dx (arcsec(u))

Answer 23

u’ / |u|root(u^2 - 1)

Question 24

d/dx (arccsc(u))

Answer 24

-u’ / |u|root(u^2 - 1)