Derivative and Integral formulae quiz

Question 1

ddx(x^n)

Answer 1

nx^(n-1)

Question 2

ddx (f +/- g)

Answer 2

f’ +/- g’

Question 3

ddx ( f x g)

Answer 3

f(g’) + g(f’)

Question 4

ddx ( f/g )

Answer 4

(g(f’) - f(g’))/g^2

Question 5

ddx (sin u)

Answer 5

cos(u) (du/dx)

Question 6

ddx (cos u)

Answer 6

• sin(u) (du/dx)

Question 7

ddx (tan u)

Answer 7

sec^2(u) (du/dx)

Question 8

ddx (sec u)

Answer 8

sec(u)tan(u) (du/dx)

Question 9

ddx (csc u)

Answer 9

• csc(u)cot(u) (du/dx)

Question 10

ddx (cot u)

Answer 10

• csc^2(x) (du/dx)

Question 11

ddx (sin^(-1) u)

Answer 11

1/( √1-u^2) (du/dx)

Question 12

ddx (cos^(-1) u)

Answer 12

-1/((√1-u^2) (du/dx)

Question 13

ddx (tan^(-1) u)

Answer 13

1/(1+u^2) (du/dx)

Question 14

ddx (csc^(-1) u)

Answer 14

-1/(abs(u)(√u^2 - 1)) (du/dx)

Question 15

ddx (sec^(-1) u)

Answer 15

1/(abs(u)(√u^2 - 1)) (du/dx)

Question 16

ddx (cot^(-1) u)

Answer 16

-1/(1+u^2) (du/dx)

Question 17

ddx (f(g(x))

Answer 17

f’(g(x)) x g’(x)

Question 18

ddx (f^(-1)(x))

Answer 18

1/(f’(f^(-1)(x)))

Question 19

ddx e^u

Answer 19

e^u x (du/dx)

Question 20

ddx a^u

Answer 20

(a^u)(ln(a)) x (du/dx)

Question 21

ddx ln(u)

Answer 21

1/(abs(u)) x (du/dx)

Question 22

ddx log(base a)(u)

Answer 22

1/(abs(u))ln(a) x (du/dx)