IB Maths AI 5.4 Definitions

This page contains our IB Maths AI definitions for 5.4. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Advanced derivatives'.

All Topic 5 Sub-topics 5.1: Introduction To Derivatives 5.2: Applying Derivatives 5.3: Fundamentals Of Integration (HL)5.4: Advanced derivatives (HL)5.5: Further integration (HL)5.6: Applying integration (HL)5.7: Kinematics (HL)5.8: Introduction to differential equations (HL)5.9: Advanced differential equations

chain rule

A differentiation rule for a composite function, used in implicit differentiation so that differentiating a term in $y$ introduces a factor of $\frac{dy}{dx}$ , for example $\frac{d}{dx}\bigl(y^2\bigr)=2y\frac{dy}{dx}$ .

composite

Describes a function formed by putting one function inside another, for example '

f\left(g\left(x\right)\right)

', which typically requires the chain rule to differentiate.

cos

A trigonometric function whose derivative is '

-\sin x

cosine

A trigonometric function whose derivative is

\frac{d}{dx}(\cos x)=-\sin x

The natural logarithm function, with derivative $\frac{1}{x}$ for $x\gt0$ .

quotient

A result of division; in a logarithmic identity this refers to combining a fraction inside a single log, such as

\log_a\left(\frac{x}{y}\right)=\log_ax-\log_ay

for suitable positive

x

and

y

quotient rule

A differentiation rule for a quotient

\frac{u}{v}

, giving

\frac{d}{dx}\left(\frac{u}{v}\right)=\frac{u'v-uv'}{v^2}

sin

A trigonometric function whose derivative is '

\cos x

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