Derivatives

Question 1

dy/dx (uv)

Answer 1

u’ v + u v’

Question 2

dy/dx (u/v)

Answer 2

(v u’ - u v’)/v^2

Question 3

dy/dx (stuff)^n

Answer 3

n(stuff)^n-1 * (stuff)’

Question 4

dy/dx sinx

Answer 4

cosx

Question 5

dy/dx cosx

Answer 5

-sinx

Question 6

dy/dx tanx

Answer 6

sec^2x

Question 7

dy/dx cscx

Answer 7

-cscxcotx

Question 8

dy/dx secx

Answer 8

secxtanx

Question 9

dy/dx cotx

Answer 9

-csc^2x

Question 10

dy/dx sin^-1x

Answer 10

1/√(1-x^2)

Question 11

dy/dx cos^-1x

Answer 11

-1/√(1-x^2)

Question 12

dy/dx tan^-1x

Answer 12

1/(1+x^2)

Question 13

dy/dx csc^-1x

Answer 13

-1/|x|√(x^2-1)

Question 14

dy/dx sec^-1x

Answer 14

1/|x|√(x^2-1)

Question 15

dy/dx cot^-1x

Answer 15

-1/(1+x^2)

Question 16

dy/dx a^u

Answer 16

a^u * ln(a) * u’

Question 17

dy/dx log base a of u

Answer 17

1/ln(a) * 1/u * u’

Question 18

dy/dx x^x

Answer 18

dy/dx (ln(y) = xln(x))