calculus: derivative

Question 1

d/dx [cu]

Answer 1

cu’

Question 2

d/dx [uv]

Answer 2

v’u + u’v

Question 3

d/dx [c]

Answer 3

0

Question 4

d/dx [x]

Answer 4

1

Question 5

d/dx [u+v]

Answer 5

u’ + v’

Question 6

d/dx [u/v]

Answer 6

(vu’ + uv’)/v^2

Question 7

d/dx [u^n]

Answer 7

nu^(n-1) * u’

Question 8

d/dx [ |u| ]

Answer 8

u/|u| * u’

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 [sin(u)]

Answer 11

cosu * u’

Question 12

d/dx [cos(u)]

Answer 12

-sinu*u’

Question 13

d/dx [tan(u)]

Answer 13

sec^2u *u’

Question 14

d/dx [csc(u)]

Answer 14

-cscucotu *u’

Question 15

d/dx [sec(u)]

Answer 15

secutanu * u’

Question 16

d/dx [cot(u)]

Answer 16

-csc^2u * u’

Question 17

d/dx [arcsin(u)]

Answer 17

u’/ square root(1 - u^2)

Question 18

d/dx [(arccosu)]

Answer 18

-u’/ square root(1 - u^2)

Question 19

d/dx [arctan(u)]

Answer 19

u’/(1 + u^2)

Question 20

d/dx [arccsc(u)]

Answer 20

-u’/(|u|*square root(u^2 - 1))

Question 21

d/dx [arcsec(u)]

Answer 21

u’/(|u|*square root(u^2 - 1))

Question 22

d/dx [arccot(u)]

Answer 22

-u’/(1 + u^2)