The Derivative (HSC SSCE Mathematics Advanced): Flashcards

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Derivatives of Basic Functions
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What does the derivative represent?

The gradient (or slope) of a function's graph

Definition of constant function

Function producing only one output value regardless of input

Graph of constant function f(x)=cf(x) = c

Horizontal line with zero gradient

Derivative of f(x)=cf(x) = c (constant)

f(x)=0f'(x) = 0

Form of linear function

y=mx+cy = mx + c

What does mm represent in y=mx+cy = mx + c?

Gradient (steepness of the line)

What does cc represent in y=mx+cy = mx + c?

y-intercept (where line crosses y-axis)

Derivative of f(x)=mx+cf(x) = mx + c

f(x)=mf'(x) = m

Why does constant cc disappear when differentiating?

Constants don't contribute to rate of change/gradient

Derivative of f(x)=xf(x) = x

f(x)=1f'(x) = 1

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