A-Level Maths Edexcel (9MA0)

1.7: Differentiation

#1.7.1

Differentiation

Differentiate from first principles

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x^n

from first principles (integer powers)

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\sin x

\cos x

from first principles

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Sketch gradient function for a given curve

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Use second derivative

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Interpret derivative as instantaneous rate of change

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#1.7.2

Differentiation rules

x^n

(positive integer powers)

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Differentiate sums, differences and multiples

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x^n

(rational powers)

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Differentiate trigonometric functions

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e^x

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\ln x

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a^x

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#1.7.3

Applications of differentiation

Find equation of tangent at a point on a curve

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Find equation of normal at a point on a curve

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Find stationary points

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Identify increasing and decreasing functions

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Identify concavity of functions

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Find points of inflection

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#1.7.4

Chain rule, product rule and quotient rule

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Use product rule

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Use quotient rule

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Differentiate reciprocal trigonometric functions

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Differentiate inverse trigonometric functions

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Solve problems involving connected rates of change

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#1.7.5

Implicit and parametric differentiation

Differentiate parametric equations

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Differentiate implicit equations

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#1.7.6

Construct simple differential equations

Construct simple differential equations

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1.6

Exponentials and logarithms

1.8

Integration

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