exam 2

Question 1

how to find the derivative of problems like e^x+2

Answer 1

its just the e term multipled by the derivative of the exponent so:

e^x+2 (1)

Question 2

how to find the derivatives of problems like 3^x

Answer 2

the same term multiplied by ln of the base so:

3^x ln(3)

Question 3

how to find the derivative of problems like 7^2x+5

Answer 3

take the full term multiplied by derivative of exponent times ln of base so:

7^2x+5 (2) ln(7)

Question 4

derivative of sin(x)

Answer 4

cos(x)

Question 5

derivative of cos(x)

Answer 5

-sin(x)

Question 6

derivative of tan(x)

Answer 6

sec^2(x)

Question 7

The graph of the tangent line when f(x) has a corner and a vertical tangent

Answer 7

• vertical tangents on f(x) = vertical asymptotes on f’(x)
• corners on f(x) = holes on f’(x)

Question 8

constant multiple rule for derivatives

Answer 8

constants can get pulled out and carried along while differentiating

(can just take the constant out and take the derivative separately)

Question 9

how to find the derivative of 4^x

Answer 9

4^x ln(4)

Question 10

difference between tangent line and normal line

Answer 10

slope of the normal line is perpendicular to the slope of the tangent line

Question 11

when is the tangent line to the graph horizontal

Answer 11

when it is equal to 0

Question 12

formula of vertex (for when object reaches highest point for parabola)

Answer 12

-b/2a

Question 13

how to know if an object is speeding up or slowing down at a specific time

Answer 13

• speeding up: signs of acceleration and velocity are the same
• slowing down: signs of acceleration and velocity are different

doesn’t matter whether both positive or both negative

Question 14

how to find anti derivative

Answer 14

add one to exponent and then divide by the new exponent

Question 15

how to do the anti derivative of 5^x

Answer 15

have to put ln(5) over 1 and then multiply by 5^x so:

1/ln(5) * 5^x

Question 16

what’s the trig identity for tan

Answer 16

sin/cos

Question 17

what’s the trig identify for sec

Answer 17

1/cos

Question 18

what’s the trig identity for csc

Answer 18

1/sec

Question 19

what is the trig identity for cot

Answer 19

cos/sin

Question 20

trig identity for sin2 + cos2

Answer 20

sin^2x + cos^2x = 1

Question 21

what to do when asked to find the exact value of cos(3π/4)

Answer 21

1. multiply 3π/4 by 180/π to find the reference angle
2. subtract or add from 180 to find the exact angle and see which quadrant it is in and whether or not it’s positive or negative
3. use that chart with all the exact values to find