Common Derivatives

Question 2

derivative

d/dx c

Answer 2

0

Question 3

derivative

d/dx x^n

Answer 3

nx^(n-1) , !(n = -1)

ln x , n = -1

Question 4

derivative

d/dx sin x

Answer 4

cos x

Question 5

derivative

d/dx cos x

Answer 5

-sin x

Question 6

derivative

d/dx tan x

Answer 6

(sec x)^2

Question 7

derivative

d/dx cot x

Answer 7

-(csc x)^2

Question 8

derivative

d/dx sec x

Answer 8

(sec x)(tan x)

Question 9

derivative

d/dx csc x

Answer 9

-(csc x)(cot x)

Question 10

derivative

d/dx sin^-1 x

Answer 10

1/sqrt(1 - x^2)

-(d/dx cos^-1 x)

Question 11

derivative

d/dx cos^-1 x

Answer 11

• 1/sqrt(1 - x^2)

- (d/dx sin^-1 x)

Question 12

derivative

d/dx sec^-1 x

Answer 12

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

-(d/dx csc^-1 x)

Question 13

derivative

d/dx csc^-1 x

Answer 13

• 1/(|x|sqrt( x^2 - 1 ))

- (d/dx sec^-1 x)

Question 14

derivative

d/dx tan^-1 x

Answer 14

1/(1 + x^2)

-(d/dx cot^-1 x)

Question 15

derivative

d/dx cot^-1 x

Answer 15

• 1/(1 + x^2)

- (d/dx tan^-1 x)

Question 16

derivative

d/dx y^x

Answer 16

(y^x)(ln y)

Question 17

derivative

d/dx log(a, x)

Answer 17

1/( x(ln a) )

Question 18

derivative

d/dx e^(ax)

Answer 18

ae^(ax)

Question 19

derivative

d/dx ln x

Answer 19

1/x

Question 20

derivative

d/dx sinh x

Answer 20

cosh x

Question 21

derivative

d/dx cosh x

Answer 21

sinh x

Question 22

derivative

d/dx tanh x

Answer 22

(sech x)^2

Question 23

derivative

d/dx csch x

Answer 23

-(csch x)(coth x)

Question 24

derivative

d/dx sech x

Answer 24

-(sech x)(tanh x)

Question 25

derivative

d/dx coth x

Answer 25

-(csch x)^2

Question 26

derivative

hyperbolic functions whose differentiation formulas are analogous to their trigonometric function counterparts

Answer 26

sinh x
csch x
tanh x
coth x

Question 27

derivative

hyperbolic functions whose differentiation formulas are analogous to their trigonometric function counterparts, but with the opposite sign

Answer 27

cosh x

sech x

Question 28

derivative

analytic formula for sinh^-1 x

Answer 28

ln( x + sqrt( x^2 + 1)), x ε R

Question 29

derivative

analytic formula for cosh^-1 x

Answer 29

ln( x + sqrt( x^2 - 1)), x >= 1

Question 30

derivative

analytic formula for tanh^-1 x

Answer 30

(1/2) ln( (1+x) / (1-x) ), -1<1

Question 31

derivative

d/dx cosh^-1 x

Answer 31

1/sqrt(x^2 - 1), x > 0

1/(sqrt(x - 1)sqrt(x + 1))

Question 32

derivative

d/dx tanh^-1 x

Answer 32

1/(1 - x^2), |x| < 1

Question 33

derivative

d/dx csch^-1 x

Answer 33

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

Question 34

derivative

d/dx sech^-1 x

Answer 34

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

Question 35

derivative

d/dx coth^-1 x

Answer 35

1/(1 - x^2), |x| > 1

Question 36

d/dx sinh^-1 x

Answer 36

1/sqrt(x^2 + 1)

Question 37

d/dx (y^x)/(ln x)

Answer 37

y^x