TOPIC 11: DIFFERENTIATION

Question 1

Differentiation of trigonometric functions

Answer 1

sin x = cos x
cos x = - sin x
tan x = sec² x

Question 2

Differentiation of sec / cosec / cot

Answer 2

sec x = sec x tan x
cosec x = - cosec x cot x
cot x = - cosec² x

Question 3

Differentiation by first principles

Answer 3

lim [ f(x+h) - f(x) / h ]

Question 4

Difference between f⁽²⁾ x and f² x

Answer 4

f⁽²⁾ x : 2nd derivative of x (dy/dx twice)
f²x : Power 2 to f(x)

Question 5

When to use implicit differentiation?

Answer 5

When cannot make y the subject

Question 6

2 main ideas of differentiation

Answer 6

1. Differentiate both sides
2. Can have both x and y in 1 term (use product / quotient rule)

Question 7

2 main ideas of differentiation

Answer 7

1. Differentiate both sides
2. Can have both x and y in 1 term (use product / quotient rule)

Question 8

Differentiation of inverse functions

Answer 8

sin⁻¹ x = 1 / √(1 - x²)
cos⁻¹ x = -1 / √(1 - x²)
tan⁻¹ x = 1 / (1 + x²)

Question 9

Differentiation of e and ln/log

Answer 9

eˣ = eˣ
aˣ = aˣ ln a (**a must be a constant)

lnx = 1 / x
logₐx = 1 / (xlna)

Question 10

Parametric differentiation

Answer 10

dy/dt = dy/dx x dx/dt

Question 11

3 Important things for differentiation

Answer 11

1. Simplify as much as possible first e.g. split ln
2. See if can convert anything to simplify based on previous workings e.g. y OR dy/dx