Differential Calculus

Question 1

Is the branch of mathematics that studies continuously changing quantities

Answer 1

Calculus

Question 2

Calculus was developed when

Answer 2

17th century

Question 3

Who developed calculus

Answer 3

Sir Isaac Newton and GW Leibniz

Question 4

Means change

Answer 4

Differential

Question 5

Means rate of change

Answer 5

Derivative

Question 6

d/dx (c)

Answer 6

0

Question 7

d/dx (cu)

Answer 7

du/dx (c)

Question 8

d/dx (u ± v)

Answer 8

du/dx ± dv/dx

Question 9

d/dx (uv)

Answer 9

dv/dx (u) + du/dx (v)

Question 10

d (u/v)

Answer 10

(du/dx (v) - d/dx (u))/v²

Question 11

d/dx (u^n)

Answer 11

nu^(n-1) du

Question 12

d √u

Answer 12

du/2√ u

Question 13

d(e)^u

Answer 13

(e^u) du

Question 14

d (a)^u

Answer 14

(ln a)a^u du

Question 15

d ln u

Answer 15

du/u

Question 16

d(loga u)

Answer 16

(loga e)/u (du)

Question 17

d (sin u)

Answer 17

cos u du

Question 18

d (cos u)

Answer 18

• sin u du

Question 19

d (tan u)

Answer 19

sec² u du

Question 20

d (cot u)

Answer 20

• csc² u du

Question 21

d (sec u)

Answer 21

sec u tan u du

Question 22

d (csc u)

Answer 22

• csc u cot u du

Question 23

d (sinh u)

Answer 23

cosh u du

Question 24

d (cosh u)

Answer 24

sinh u du

Question 25

d (tanh u)

Answer 25

sech² u du

Question 26

d (cothbu)

Answer 26

- csch² u du

Question 27

d (sech u)

Answer 27

- sech u tanh u du

Question 28

d (csch u)

Answer 28

- csch u coth u du

Question 29

d (sin^-1 u)

Answer 29

du/(√(1-u²))

Question 30

d (cos^-1 u)

Answer 30

-du/(√(1-u²))

Question 31

d (tan^-1 u)

Answer 31

du/(1+u²)

Question 32

d (cot^-1 u)

Answer 32

- du/(1+u²)

Question 33

d (sec^-1 u)

Answer 33

du/(u√(u² -1))

Question 34

d (csc^-1 u)

Answer 34

- du/(u√(u² -1))