Differentiation

Question 1

Dx (sin x)

Answer 1

cos x

Question 2

Dx (tan x)

Answer 2

sec² x

Question 3

Dx(sec x)

Answer 3

sec x tan x

Question 4

Dx(cos x)

Answer 4

-sin x

Question 5

Dx(cot x)

Answer 5

-csc² x

Question 6

Dx (csc)

Answer 6

-csc x cot x

Question 7

Dx (e^x)

Answer 7

e^x

Question 8

Dx (a^x)

Answer 8

a^x ln a

Question 9

Dx (sin^-1 u)

Answer 9

1/√1-u^2 Dx u

Question 10

Dx (tan-¹ u)

Answer 10

1/1+u^2 Dx u

Question 11

Dx (sec^-1 u)

Answer 11

1/u√u^2-1 Dx u

Question 12

Dx (cos-¹ u)

Answer 12

-(1/√1-u^2) Dx u

Question 13

Dx (cot^-1 u)

Answer 13

-(1/1+u^2) Dx u

Question 14

Dx (csc^-1 u)

Answer 14

-(1/u√u^2-1) Dx u

Question 15

Dx (sinh u)

Answer 15

cosh u Dx u

Question 16

Dx (tanh u)

Answer 16

sech^2 u Dx u

Question 17

Dx (sech u)

Answer 17

sech u tanh u Dx u

Question 18

Dx (cosh u)

Answer 18

sinh u Dx u

Question 19

Dx (coth u)

Answer 19

-csch^2 u Dx u

Question 20

Dx (csch u)

Answer 20

-csch u coth u Dx u

Question 21

Dx (sinh-¹ u)

Answer 21

1/√u²+1 Dx u

Question 22

Dx (tanh-¹ u)

Answer 22

1/1-u² Dx u

Question 23

Dx (sech-¹ u)

Answer 23

-1/u√1-u² Dx u

Question 24

Dx (cosh-¹ u)

Answer 24

1/√u²-1 Dx u

Question 25

Dx (coth-¹ u)

Answer 25

1/1-u² Dx u

Question 26

Dx (csch-¹ u)

Answer 26

1/|u|√u² + 1 Dx u

Question 27

Dx (ln u)

Answer 27

1/u Dx

Question 28

Dx (log a u)

Answer 28

1/u (ln a) Dx u

Question 29

product rule, quotient rule

Answer 29

udv + vdu , lodhi - hidlo/lo²

Question 30

Dx[f(u)]

chain rule

Answer 30

f’(u) Dx u