OEF derivative --- Introduction ---

In this module there are 6 exercices on differentiation .

The derivative of a combined function

Given the function :
Determine the derivative in

NB : write "sqrt(ax+b)" for

The derivative of a polynomial

Let be a polynomial , gedefined in by .

Let be differentiable in . Determine the derivative.

For all real , =

The product rule

Determine the derivative of a function in defined by with :

The functions and are differentiable in and : = =

In order to determine the derivative of we apply the following rule of differentiation:

The derivative function of will be :

The quotient rule

Given the function defined in by .

We will now determine the derivative of in a few steps :

We rewrite as a fraction; ,wherein the functions and are defined in by : and
The functions and are differentiable in : and
= met :
en
and
The fraction is differentiable in:
Which rule on differentiation do we apply :
is differentiable in .
Which rule on differentiation do we apply :
We will get : =

Tangent and derivative

Given the plane .

The curve C is the graph of the function , defined in .

The line is the tangent of C in point , with coordinates ( : ).

Point , with coordinates ( : ) is also on line .
Determine the value of at two decimals accurate.

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Investigate a Function

Given the function defined in

by .

Investigate this function and determine the extremum (extrema) of .

The function is differentiable in :
for all real
The nature of the derivative function is zero for =

The derivative of
The nature of the sign of - + 0
The nature of the sign of is on the interval
is on the interval

The extremum of reaches in a with value

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Description: practising with differentiation. interactive exercises, online calculators and plotters, mathematical recreation and games at University of Chieti-Pescara
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