Derivatives

Question 1

Dx (cos x)

Answer 1

-sin x

Question 2

Dx (ln x)

Answer 2

1/x

Question 3

Dx (f x g)

Answer 3

f’g + fg’

Question 4

Dx (csc x)

Answer 4

-csc x cot x

Question 5

Dx (e^x)

Answer 5

e^x

Question 6

Dx (e^u)

Answer 6

(e^u)(u’)

Question 7

Dx (tan x )

Answer 7

sec^2(x)

Question 8

Dx (f/g)

Answer 8

(f’g-fg’)/g^2

Question 9

Dx (arcsin x)

Answer 9

1/(sqroot(1-x^2))

Question 10

Dx (arcsin u)

Answer 10

u’/(sqroot(1-u^2))

Question 11

Dx (ln abs(u))

Answer 11

u’/u

Question 12

Dx (x^n)

Answer 12

nx^n-1

Question 13

Dx (arctan x)

Answer 13

1/(1+x^2)

Question 14

Dx (arctan u)

Answer 14

u’/(1+u^2)

Question 15

Dx (sin x)

Answer 15

cos x

Question 16

Dx (arcsec x)

Answer 16

1/(abs(x) sqroot((x^2)-1))

Question 17

Dx (arcsec u)

Answer 17

u’/(abs(u) sqroot((u^2)-1))

Question 18

Dx (cot x)

Answer 18

-csc^2(x)

Question 19

Dx (arccos x)

Answer 19

-x/(sqroot(1-x^2))

Question 20

Dx (arccos u)

Answer 20

-u’s(sqroot(1-u^2))

Question 21

Dx (sec x)

Answer 21

(sec x)(tan x)

Question 22

Dx (f(g(x)))

Answer 22

f’(g(x))(g’(x))

Question 23

Dx (f(x) +/- g(x))

Answer 23

f’(x) +/- g’(x)

Question 24

Dx (c)

Answer 24

0