Page 3 - PRE-U STPM MATHEMATICS (T) TERM 2

CHAPTER
2 DIFFERENTIATION

Subtopic Learning Outcome

2.1 Derivatives (a) Identify the derivative of a function as a limit.
(b) Find the derivatives of x (n  Q), e , In x, sin x, cos x, tan x, sin x, cos x,
–1
n
–1
x
tan –1 x, with constant multiples, sums, differences, products, quotients and
composite.
(c) Perform implicit differentiation.
(d) Find the first derivatives of functions defined parametrically.
2.2 Applications of (a) Determine where a function is increasing, decreasing, concave upward and
differentiation concave downward.
(b) Determine the stationary points, extremum points and points of inflexion.
(c) Sketch the graphs of functions, including asymptotes parallel to the coordinate
axes.
(d) Find the equations of tangents and normals to curves, including parametric
curves.
(e) Solve problems concerning rates of change, including related rates.
(f) Solve optimisation problems.

Bilingual Keywords

asymptote – asimptot
concave downward – cekung ke bawah
curve – lengkung
decreasing – menyusut
derivative – terbitan
differentiation – pembezaan
extremum point – titik ekstremum
implicit function – fungsi tersirat
increasing – menokok
limit – had
point of inflexion – titik lengkok balas
stationary point – titik pegun

02 STPM Math(T) T2.indd 16 02/11/2018 12:43 PM