Important rules to remember for chapter 3

Question 1

Derivate of e^x is

Answer 1

e^x

Question 2

(fg) prime is

Answer 2

fg^’ + gf^’

Question 3

f/g prime si

Answer 3

gf^’ - fg^’/g^2

Question 4

Sometimes it is easier to do what to a quotient rule?

Answer 4

REWRITE

Question 5

Derivative of sinx

Answer 5

cosx

Question 6

Derivative of cosx

Answer 6

-sinx

Question 7

Derivative of tanx

Answer 7

sec^2x

Question 8

Derivative of cscx

Answer 8

-cscx * cotx

Question 9

Derivative of secx

Answer 9

secx * tanx

Question 10

Derivative of cotx

Answer 10

-csc^2x

Question 11

What is the chain rule

Answer 11

f^’(g(x)) * g^’(x)

Question 12

Derivative of logbx

Answer 12

1/x ln b

Question 13

Derivative of lnx

Answer 13

1/x

Question 14

What are the steps of Logarithmic Differentiation?

Answer 14

1. Take natural logarithms of both sides of an equation y =f(x) and use the Laws of Logarithms to simplify
2. Differentiate implicitly with respect to x
3. Solve the resulting equation for y^’

Question 15

Growth and Decay Equation

Answer 15

y(t) = y(0)e^kt

Question 16

Radioactive Decay

Answer 16

m(t) = m0e^kt

Question 17

Linear Approximation

Answer 17

L(x) = f(a) + f’(a)(x-a)

Question 18

Differential Equation

Answer 18

dy = f’(x)dx

Question 19

Triangle Y Equation

Answer 19

f(x + <>x) - f(x)

Question 20

sinh x

Answer 20

e^x - e^x-x / 2