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Differentiation
O-Level A Math
Algebraic Expressions
$$\dfrac{d}{dx}(ax^n) = anx^{n-1}$$
Trigonometric Expressions
$$\dfrac{d}{dx}\sin x = \cos x$$
$$\dfrac{d}{dx}\cos x = -\sin x$$
$$\dfrac{d}{dx}\tan x = \sec^2 x$$
Exponential Expressions
$$\dfrac{d}{dx}e^x = e^x$$
Logarithmic Expressions
$$\dfrac{d}{dx}\ln x = \dfrac{1}{x}$$
Chain Rule
$$\dfrac{dy}{dx} = \dfrac{dy}{du} \times \dfrac{du}{dx}$$
Use when differentiating a
function of a function
, e.g. $\sin(3x^2)$ or $e^{x^2}$
Product Rule
$$\dfrac{d}{dx}(uv) = u\dfrac{dv}{dx} + v\dfrac{du}{dx}$$
Use when differentiating a
product
of two functions, e.g. $x^2 \sin x$
Quotient Rule
$$\dfrac{d}{dx}\!\left(\dfrac{u}{v}\right) = \dfrac{v\,\dfrac{du}{dx} - u\,\dfrac{dv}{dx}}{v^2}$$
Use when differentiating a
quotient
of two functions, e.g. $\dfrac{\sin x}{x}$
Formulas for the Singapore O-Level Additional Mathematics syllabus