Derivative

Question 1

π

Answer 1

0

Question 2

x

Answer 2

1

Question 3

f(x) = 2x^3 - 5x^2 +3x -2

Answer 3

6x^2 - 10x +3

Question 4

f(x)g(x)

Answer 4

f’(x)g(x) + f(x)g’(x)

Question 5

f(x)/g(x)

Answer 5

(f’(x)g(x) - f(x)g’(x)) / (g(x)^2)

Question 6

f(x)^u

Answer 6

u(f(x)^u-1)(u’)

Question 7

Sinx

Answer 7

Cosx

Question 8

Cosx

Answer 8

-sinx

Question 9

Sin^2(x)

Answer 9

f(x) = (sinx)^2
f’(x) = 2sinxcosx

Question 10

√u

Answer 10

(1/2)u^(-1/2) u’

Question 11

e^u

Answer 11

(e^u) u’

Question 12

a^u

Answer 12

ln(a) (a^u) u’

Question 13

loga^u

Answer 13

(1/ u ln(a)) u’

Question 14

tanx

Answer 14

sec^2(x)

Question 15

csc(x)

Answer 15

-csc(x)cot(x)

Question 16

sec(x)

Answer 16

sec(x)tan(x)

Question 17

cot(x)

Answer 17

-csc^2(x)

Question 18

ln(u)

Answer 18

(1/u) u’

Question 19

ln(u)

Answer 19

(1/u) u’

Question 20

f(x) using a limit

Answer 20

(Lim h->0) (f(x-h) - f(x)) / h

Question 21

sin^-1(x)

Answer 21

1/√(1-x^2)

Question 22

cos^-1(x)

Answer 22

-1/√(1-x^2)

Question 23

tan^-1(x)

Answer 23

1/(1+ x^2)

Question 24

cot^-1(x)

Answer 24

-1/(1+ x^2)

Question 25

csc^-1(x)

Answer 25

-1/(x√((x^2) -1))

Question 26

sec^-1(x)

Answer 26

1/(x√((x^2) -1))

Question 27

When to use squeeze theory

Answer 27

With trig
example: -1 < sinx < 1

Question 28

|a| > x

Answer 28

-x > a > x

Question 29

When to use l`hospital rule

Answer 29

0/0 or (+/-infinite)/(+/-infinite)

Question 30

(d/dx)y^2 = (d/dx)x + (d/dx)5

Answer 30

(dy/dx)y = 1 + 0

Question 31

L’hospital equation

Answer 31

(Lim x->a) f(x)/g(x) = (Lim x->a) f’(x)/g’(x)

Question 32

L’hospital equation

Answer 32

(Lim x->a) f(x)/g(x) = (Lim x->a) f’(x)/g’(x)