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Differentiation

A-Level H2 Math

Trigonometric & Inverse Trigonometric

Trigonometric

$\dfrac{d}{dx}\tan x = \sec^2 x$

$\dfrac{d}{dx}\cot x = -\csc^2 x$

$\dfrac{d}{dx}\sec x = \sec x \tan x$

$\dfrac{d}{dx}\csc x = -\csc x \cot x$

Inverse Trigonometric

$\dfrac{d}{dx}\sin^{-1} x = \dfrac{1}{\sqrt{1-x^2}}$

$\dfrac{d}{dx}\cos^{-1} x = -\dfrac{1}{\sqrt{1-x^2}}$

$\dfrac{d}{dx}\tan^{-1} x = \dfrac{1}{1+x^2}$

Exponential & Logarithmic

Exponential

$\dfrac{d}{dx}e^x = e^x$

$\dfrac{d}{dx}a^x = a^x \ln a$

Logarithmic

$\dfrac{d}{dx}\ln x = \dfrac{1}{x}$

$\dfrac{d}{dx}\log_a x = \dfrac{1}{x\ln a}$

Formulas for the Singapore A-Level H2 Mathematics syllabus