IB Maths AA 5.9 Definitions

This page contains our IB Maths AA definitions for 5.9. By learning each one of these definitions, you will fully cover the content for IB Maths AA 'Challenging derivatives'.

All Topic 5 Sub-topics 5.1: Introduction To Derivatives 5.2: Applying Derivatives 5.3: Advanced Derivatives 5.4: Introduction To Integration 5.5: Advanced Integration 5.6: Kinematics (HL)5.7: Advanced limits (HL)5.8: Implicit differentiation (HL)5.9: Challenging derivatives (HL)5.10: Challenging integration (HL)5.11: Applying integration (HL)5.12: Differential equations (HL)5.13: Maclaurin series

arccos

The inverse function of cosine that returns the principal angle '

y

' such that '

\cos y=x

', with domain '

-1\leq x\leq1

' and output values '

0\leq y\leq\pi

arcsin

An inverse trigonometric function whose derivative is

\frac{d}{dx}\left(\arcsin x\right)=\frac{1}{\sqrt{1-x^2}}

, and for an input

f(x)

becomes

\frac{f'(x)}{\sqrt{1-\left(f(x)\right)^2}}

arctan

The inverse function of tangent that returns the principal angle '

y

' such that '

\tan y=x

', with domain all real numbers and output values '

-\frac{\pi}{2}\lt y\lt\frac{\pi}{2}

cosec

A reciprocal trigonometric ratio defined by '

\cosec x=\frac{1}{\sin x}

', so it is undefined where '

\sin x=0

cot

A reciprocal trigonometric function whose derivative is

\frac{d}{dx}\left(\cot x\right)=-\cosec^2 x

, and for an input

f(x)

becomes

-\cosec^2\left(f(x)\right)f'(x)

log

A logarithmic function with base

a

whose derivative is

\frac{d}{dx}\left(\log_a x\right)=\frac{1}{x\ln a}

, and for an input

f(x)

becomes

\frac{f'(x)}{f(x)\ln a}

sec

A reciprocal trigonometric function whose derivative is

\frac{d}{dx}\left(\sec x\right)=\sec x\tan x

; for an input

f(x)

\frac{d}{dx}\left(\sec\left(f(x)\right)\right)=\sec\left(f(x)\right)\tan\left(f(x)\right)f'(x)

tan

Defined by

\tan\theta=\frac{\sin\theta}{\cos\theta}

, so it is undefined whenever

\cos\theta=0

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