Unit 4

Question 1

What is the product rule with differentiation?

Answer 1

f(x)=uv (separate functions)

f’(x)= u’v + uv’

Question 2

What is the quotient rule in differentiation?

Answer 2

f(x)= u/v (separate functions)
f’(x)= u’v - uv’ / v^2

Question 3

What is the chain rule in differentiation?

Answer 3

y= f(g(x))
dy/dx= f’(g(x)) • g’(x)

Question 4

What is the derivative of e^x?

What about e^(g(x))?

Answer 4

Dy/dx= e^x

Dy/dx= e^g(x) • g’(x)

Question 5

What is the derivative of a^x?

What about a^(g(x))?

Answer 5

Da^x/dx= (ln a)a^x

da^(g(x))/dx= a^g(x) • (g’(x)) • ln a

Question 6

What is the derivative of loga(x)?

Answer 6

D(loga(x))/dx= 1/ (ln a)x

Question 7

What is the derivative of

loga|g(x)| ?

Answer 7

1/ln a • (g’(x)/g(x))

Question 8

What is the derivative of ln |x|?

Answer 8

1/x

Question 9

What is the derivative of ln|g(x)|?

Answer 9

G’(x)/g(x)

Question 10

What is the trigonometry identity involving sin2x, cos2x and 1?

Answer 10

Sin2x + cos2x = 1

Question 11

What is sin(x+y) equal to? What about sin(x-y)?

Answer 11

Sin(x+y)=sinxcosy + cosxsiny

Switch + to - when x-y

Question 12

What is cos(x+y)? What about cos(x-y)?

Answer 12

Cos(x+y)=cosxcosy - sinxsiny

Switch - to + for x-y

Question 13

What is the derivative of sinx?
Cosx?
Tanx?

Answer 13

Sinx- cosx
Cosx- -sinx
Tanx- sec2(x)

Question 14

How can you prove the derivative of sinx?

Answer 14

Use sin as f in the complex derivative equation:
Lim f(x+h)-f(x) / h
H->0

Question 15

What is the derivative of cotx?
Secx?
Cscx?

Answer 15

Cotx- -csc2(x)
Secx- secxtanx
Cscx- -cscxcotx