# Derivatives

### Terms

### Derivative Of A Function

The measurement of how*f*(

*x*) changes at a point

*x*.

### Slope Of A Line

The change in the*y*-value of the line for a unit change in the

*x*value.

### Average Rate Of Change

The change in the function*f*(

*x*) as

*x*changes over an interval [

*a*,

*b*].

### Instantaneous Rate Of Change

The change in the function*f(x)*at a point

*x*.

### Secant Line

A line joining two points on the graph of a function.### Tangent Line

A line that touches the graph of a function*f*(

*x*) at a point.

### Differentiability

If the limit \lim_{h\to 0}\frac{f(a+h)-f(a)}{h} exists, the function*f*(

*x*) is differentiable at

*x*=

*a*.

### Vector

A mathematical structure that has both magnitude and direction, represented by an ordered pair of components.### Magnitude Of A Vector

The length of a vector, denoted by || ||.### Direction Of A Vector

The counter-clockwise angle from the positive*x*-axis to the vector.

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