Exam Prep

Question 1

What’s the derivative of y=arctan(x)

Answer 1

y’=1/(1+x^2)

Question 2

What’s the derivative of y=csc(x)

Answer 2

y’= (-csc(x)) (cot(x))

Question 3

whats the derivative of y=sec(x)

Answer 3

y’= (sec(x)) x (tan(x))

Question 4

whats the derivative of y = cos(x)

Answer 4

y’= -sin(x)

Question 5

Whats the derivative of y = sin(x)

Answer 5

y’= cos(x)

Question 6

what is the quotient rule?

Answer 6

(f’(X) x g(x) - f(x) x g’(x)) / [g(x)]^2

Question 7

What’s the derivative of y = arccos(x)

Answer 7

y’= -1/(sqrt 1-x^2)

Question 8

what’s the derivative of y = cot(x)?

Answer 8

y’= -csc^2(x)

Question 9

What’s the derivative of y = tan(x)

Answer 9

y’= sec^2(x)

Question 10

whats the derivative of y = arcsec(x)

Answer 10

y’= 1/ (|x| sqrt x^2-1)

Question 11

whats the derivative of y = arccsc(x)

Answer 11

y’= -1/ (|x| sqrt x^2 -1)

Question 12

whats the formula used to find the area of a cone?

Answer 12

A= pi r ^2 + pi r sqrt (h^2+r^2)

Question 13

What’s the derivative of y = arccot(x)

Answer 13

y’= -1/ (1+x^2)

Question 14

Whats the derivative of y = arcsin(x)

Answer 14

1/ (sqrt 1-x^2)

Question 15

f(x)=c

Answer 15

f’(x)=0

Question 16

f(x)=x^2+12x

Answer 16

f’(x)=2x+12

Question 17

f(x)=x^(2/3)

Answer 17

f’(x)=2/3x^(-1/3)

Question 18

f(x)=x^-2

Answer 18

f’(x)=-2x^(-3)

Question 19

(cf(x))’

Answer 19

c(f’(x))

Question 20

Simplification Rules

Answer 20

-use trig identities where possible
-Pythagorean theorem
-sum/difference
-double
-half

Question 21

f(x)=e^x

Answer 21

f’(x)=e^x

Question 22

f(x)=ln(x)

Answer 22

f’(x)=1/x

Question 23

f(x)=2^x

Answer 23

f’(x)=(2^x) (ln(2))

Question 24

f(x)= log2(x)

Answer 24

f’(x)= (1/x) (1/ln(2))

Question 25

f(x)= ln(x) = log e(x)

Answer 25

f'(x) = 1/x

Question 26

Derivative of g(h(x))

Answer 26

g’(h(x)) • h’(x)