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# Derivatives

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by

## Bayleigh Young

on 10 January 2014

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#### Transcript of Derivatives

Derivatives
Derivatives
Definition of a Derivative:
The derivative of the function
f
with the respect to the variable
x
is the function
f'
whose value at
x
is

provided that the limit exists.
Power Rule
Product Rule
Quotient Rule
lo de hi - hi de lo
--------------------
lo squared
Chain Rule
1. Corner
A function will not have a derivative at a point
P(a,f(a))
where the slopes of the secant lines,

fail to approach
a
limit as
x
approaches
a
.

2.Cusp
3.Vertical Tangent
4. Discontinuity
-Jump (piecewise)
-Removable (hole)
-Infinite (asymptote)
where the one-sided derivatives differ
where the slopes of the secant lines approach infinity from one side and negative infinity from the other side
where the slopes of the secant lines approach either infinity or negative infinity from both sides
cause one or both of the one-sided derivatives to be nonexistent
take the exponent and multiply it with the coefficient
take the exponent and subtract one
derivative = 1st term(
u
) * derivative of 2nd term(
dv
) + 2nd term (
v
)* derivative of 1st term(
du
)
1st term
derivative of 1st term
2nd term
derivative of 2nd term
denominator squared
derivative of the denominator
numerator

derivative of nurmerator
(denominator (
v
) * derivative of numerator(
du
) - (numerator(
u
) * derivative of numerator(
dv
)
------------------------------------------------------------------------------------------------------------------
denominator squared
little trick:
derivative= power rule * derivative of what is inside the ()
power rule
derivative of ()
Example of Infinte:
denominator
Full transcript