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Rate of Change
dxdy is the rate of change of y with respect to x.
Example:
is the rate of change in volume with respect to the radius.
Slope as a Limit
Informal understanding of slope as the limit of
as (x2−x1) goes to zero.
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Gradient
For a curve y=f(x), f′(x) is the gradient or slope.
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Example:
⇒ The slope of y=f(x) when x=1 is f′(2)=3⋅12−1=2.
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