Derivatives

Question 1

d/dx c , c = const

Answer 1

0

Question 2

d/dx x^a , a = const

Answer 2

ax^(a-1)

Question 3

d/dx x

Answer 3

1

Question 4

d/dx 1/x

Answer 4

-1/x^2

Question 5

d/dx x^(1/2)

Answer 5

1/(2x^(1/2))

Question 6

d/dx sinx

Answer 6

cosx

Question 7

d/dx cosx

Answer 7

-sinx

Question 8

d/dx tanx

Answer 8

1/cos^(2)x

Question 9

d/dx cotx

Answer 9

-1/(sin^(2)x)

Question 10

d/dx arcsinx

Answer 10

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

Question 11

d/dx arccosx

Answer 11

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

Question 12

d/dx arctanx

Answer 12

1/(1+x^(2))

Question 13

d/dx arccotx

Answer 13

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

Question 14

d/dx a^x

Answer 14

a^(x)ln(a)

Question 15

d/dx e^x

Answer 15

e^x

Question 16

d/dx loga(x)

Answer 16

1/xln(a)

Question 17

d/dx ln(x)

Answer 17

1/x

Question 18

d/dx sinhx

Answer 18

coshx

Question 19

d/dx coshx

Answer 19

sinhx

Question 20

d/dx tanhx

Answer 20

1/cosh^(2)x

Question 21

d/dx cothx

Answer 21

-1/(sinh^(2)x)

Question 22

d/dx |x|

Answer 22

sign(x)