Common Différentiels

Question 1

d/dx [sin(x)]

Answer 1

cos(x)

Question 2

d/dx [cos(x)]

Answer 2

-sin(x)

Question 3

d/dx [tan(x)]

Answer 3

sec²(x)

1/cos²(x)

Question 4

d/dx [sec(x)]

Answer 4

tan(x)sec(x)

sin(x)/cos²(x)

Question 5

d/dx [csc(x)]

Answer 5

-cot(x)csc(x)

-cos(x)/sin²(x)

Question 6

d/dx [arcsin(x)]

Answer 6

1/√(1-x²)

Question 7

d/dx [arccos(x)]

Answer 7

-1/√(1-x²)

Question 8

d/dx [arctan(x)]

Answer 8

1/1+x²

Question 9

d/dx [eˣ]

Answer 9

eˣ

Question 10

d/dx [in(x)]

Answer 10

1/x

Question 11

d/dx [xˣ]

Answer 11

xˣ[lnx + 1]

Question 12

d/dx [eⁿˣ]

Answer 12

neⁿˣ

Question 13

d/dx [eⁿ⁻ˣ]

Answer 13

-eⁿ⁻ˣ

Question 14

d/dx [ceˣⁿ]

Answer 14

cnxⁿ⁻¹eˣⁿ

Question 15

d/dx [in(5+x)]

Answer 15

1/5+x

Question 16

d/dx [cot(x)]

Answer 16

-csc²(x)

-1/sin²(x)

Question 17

d/dx [arccotx]

Answer 17

-1/1+x²

Question 18

d/dx [arcsecx]

Answer 18

1/|x|√(x²-1)

Question 19

d/dx [arccscx]

Answer 19

-1/|x|√(x²-1)

Question 20

d/dx [bˣ]

Answer 20

bˣ ⋅ ln(b)

Question 21

d/dx [logₐ(x)]

Answer 21

1/xln(a)