Differentiation (AQA A-Level Mathematics): Flashcards

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First Principles Differentiation
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First principles gradient formula

limh0F(x+h)F(x)h\lim_{h \to 0} \frac{F(x+h) - F(x)}{h}

What happens to chord as h0h \to 0

Becomes a tangent

Gradient of y=x2y = x^2

2x2x

Gradient formula for F(x)=xnF(x) = x^n, nRn \in \mathbb{R}

nxn1nx^{n-1}

Gradient of y=x4y = x^4

4x34x^3

Alternative names for gradient function

Differential, first differential, derivative, first derivative, gradient function, rate of change

How to pronounce dydx\frac{dy}{dx}

dydy by dxdx

In f(x)f'(x), what do dashes indicate?

Number of times differentiated

Derivative of x2+2xx^2 + 2x by first principles

2x+22x + 2

First step in first principles method

Draw a chord between two points on curve

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