TOPIC 11: DIFFERENTIATION Flashcards

1
Q

Differentiation of trigonometric functions

A

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

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2
Q

Differentiation of sec / cosec / cot

A

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

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3
Q

Differentiation by first principles

A

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

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4
Q

Difference between f⁽²⁾ x and f² x

A

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

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5
Q

When to use implicit differentiation?

A

When cannot make y the subject

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6
Q

2 main ideas of differentiation

A
  1. Differentiate both sides
  2. Can have both x and y in 1 term (use product / quotient rule)
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7
Q

2 main ideas of differentiation

A
  1. Differentiate both sides
  2. Can have both x and y in 1 term (use product / quotient rule)
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8
Q

Differentiation of inverse functions

A

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

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9
Q

Differentiation of e and ln/log

A

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

lnx = 1 / x
logₐx = 1 / (xlna)

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10
Q

Parametric differentiation

A

dy/dt = dy/dx x dx/dt

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11
Q

3 Important things for differentiation

A
  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
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