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# Definition of the Derivative

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## Collin Campos

on 7 December 2014

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#### Transcript of Definition of the Derivative

Definition of the Derivative
Example 2
Definition of the Derivative of a Function
The derivative of with respect to x is the function and is defined as,

Example
Example 2
Alternative Definition: Derivative at a Point
Let y = f(x) be a function and suppose that a is in the domain of f. The derivative of f at x = a is the limit
Example

Determine whether f(x) = 3 - 4x2 is differentiable at a = 5. If so, compute f '(5)

lim
h-->0
(f(5 + h) - f(5))/
h
=
lim
h-->0
(3 - 4(5 + h)^2 - (3 - 4(5)^2))/
h

=
(3 - 4(25 +10h + h2) - (3 - 4(25)))/
h

=
(-4h(10 + h))/
h

= -4(10 + h)
Full transcript