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# Differentiating Polynomial Equations

This process is basically finding the derivative function of a polynomial equation. In order to do this, the polynomial equation needs to be transformed into a function of its derivative, which is a process known as differentiation.

by

Tweet## Donald Olson

on 21 April 2010#### Transcript of Differentiating Polynomial Equations

Differentiating Polynomial Equations Lets learn the basics for finding the derivative of a function by working with a very simple equation. In this case, we'll use a polynomial equation. For the polynomial equation:

Begin by moving all exponents in front of its multiple.

This will make the exponent 2 into a coefficient.

turns into The equation turned into: which equals

For each exponent that is moved, a new exponent must replace the old one

and that new exponent must be exactly one less than the old exponent.

turns into For the next step, we need to make values that originally

had an exponent of one into the constant in front of the multiple. From our original equation:

We need to transform 2x into 2.

We can place this back into our developing deviation which will turn

into The final step is to eliminate all values

that are NOT multiplied by x. From the original equation:

We need to transform 7 into 0.

We can place this back into our developing deviation which will turn

into By comparison, we can see that the equation

has a derivative equation of We can even take the second derivative of

by using the first derivative, which will result in There are many methods for determining the derivative

of a function that must me used for functions that are more

complex than polynomial equations. These names consist

of the chain rule, the product rule, and the quotent rule. When comparing rates to functions and their derivatives,

Position is the original function

Velocity is the first derivative

Acceleration is the second derivative Now its your turn! Try In the next slide, a function and its derivative function graphed on the same plane. Notice that for each horizontal asymptote on the original function (blue), the derivative function (red) crosses the x-axis.

Full transcriptBegin by moving all exponents in front of its multiple.

This will make the exponent 2 into a coefficient.

turns into The equation turned into: which equals

For each exponent that is moved, a new exponent must replace the old one

and that new exponent must be exactly one less than the old exponent.

turns into For the next step, we need to make values that originally

had an exponent of one into the constant in front of the multiple. From our original equation:

We need to transform 2x into 2.

We can place this back into our developing deviation which will turn

into The final step is to eliminate all values

that are NOT multiplied by x. From the original equation:

We need to transform 7 into 0.

We can place this back into our developing deviation which will turn

into By comparison, we can see that the equation

has a derivative equation of We can even take the second derivative of

by using the first derivative, which will result in There are many methods for determining the derivative

of a function that must me used for functions that are more

complex than polynomial equations. These names consist

of the chain rule, the product rule, and the quotent rule. When comparing rates to functions and their derivatives,

Position is the original function

Velocity is the first derivative

Acceleration is the second derivative Now its your turn! Try In the next slide, a function and its derivative function graphed on the same plane. Notice that for each horizontal asymptote on the original function (blue), the derivative function (red) crosses the x-axis.