Math Glossary
Derivative
Definition #1
The derivative of a function, f(x), is the function that when given a value for x, say c, returns the slope of the line tangent to the curve of y=f(x) at the point ( c, f(c) ).
Definition#2
The derivative of a function, f(x), is define by
Notations for the derivative of y=f(x) are
y'
f '(x)
Dx[f(x)]
The derivative of a derivative is called a second derivative, and for y=f(x) is denoted by
y''
f ''(x)
Examples:
For f(x)=x2,
Thus, the line tangent to the curve of y=x2 at the point (3,9) would be
m=f '(3)=2(3)=6.
Hence, the equation of the tangent line would be
| y-9 | = | 6(x-3) |
| y-9 | = | 6x-18 |
| y | = | 6x-9 |
See also: difference quotient
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