Given the function :
Determine the derivative in |

=

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

Let be a polynomial , gedefined in by . Let be differentiable in . Determine the derivative. |

Determine the derivative of a function in defined by with : |

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

The derivative function of will be :

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 :
= - 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

Given the plane . The curve The line
is the tangent of Point
, with coordinates ( : ) is also on line
. | |

Given the function
defined in by
. Investigate this function and determine the extremum (extrema) of . |

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- Description: practising with differentiation. Serveur Wims de l'ESPE-Nice-Toulon - Université de Nice - Sophia Antipolis
- Keywords: interactive mathematics, interactive math, server side interactivity, mathematics, analysis,, derivative,slope,differentiation,quotientrule,productrule