CAIE: A Level - Mathematics 9709 - Pure Mathematics 3

Differentiation / Simple Differentiation

KEYPOINTS:

EXPONENTIAL FUNCTIONS

If y = e^f(x), then \(\frac{dy}{dx}\) = f’(x).e^f(x)

LOGARITHMIC FUNCTIONS

If y = ln x, then \(\frac{dy}{dx}\) = \(\frac{1}{x}\)
If y = ln[f(x)], then \(\frac{dy}{dx}\) = \(\frac{f’(x)}{f(x)}\)

TRIGONOMETRIC FUNCTIONS

If y = sin x, then \(\frac{dy}{dx}\) = cos x
If y = cos x, then \(\frac{dy}{dx}\) = –sin x
If y = tan x, then \(\frac{dy}{dx}\) = sec²x
If y = tan^–1x, then \(\frac{dy}{dx}\) = \(\frac{1}{1+x^2}\)

PRODUCT RULE

If y = ab, then \(\frac{dy}{dx}\) = a\(\frac{db}{dx}\) + b\(\frac{da}{dx}\)

QUOTIENT RULE

If y = \(\frac{a}{b}\), then \(\frac{dy}{dx}\) = \(\frac {b\frac{da}{dx}–a\frac{db}{dx}}{b^2}\)

Past Papers Topic Wise Questions A Level: Mathematics 9709 - Pure Mathematics 3 Differentiation | Simple Differentiation

1

Marking Scheme

2

Marking Scheme

3

Marking Scheme

4

Marking Scheme

The questions available on this website are the sole intellectual property of cambridgeinternational.org Our role is to curate these questions into organized topics, with the intention of benefiting students.