Wierd Q to take a derivative of

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In summary, the conversation discusses the process of taking the derivative of a complex function, specifically y=(x)/((x+2)(x+3)(x+4)). Different methods, such as the quotient's derivative rule and Leibniz product rule, are suggested. The conversation also includes a warning against multiple posting. Ultimately, the easiest way to solve the problem is by simplifying the function and using the product rule and the derivative of a reciprocal function.
  • #1
the4thcafeavenue
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wierd Q to take a derivative of...

y=(x)/((x+2)(x+3)(x+4)).
how to do u take the derivative? HELP! :confused:
 
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  • #2
So is it

[tex] y(x)=\frac{x}{(x+2)(x+3)(x+4)} [/tex]

Do u know to apply the

1.Quotient's derivative rule.
2.Leibniz product rule...?

Daniel.
 
  • #3
AARGH!

DO NOT DOUBLE, TRIPLE, OR QUADRUPLE POST IN THE FUTURE!
:grumpy:
 
  • #4
The easiest way would be to rewrite it like this first:

y=(x) * (x+2)(^-1) * (x+3)(^-1) * (x+4)(^-1)
 
  • #5
haha, i guess i'd get mroe help dat way, but, oops hehe
 
  • #6
the easiest way is actually probably to just multiply out the denominator:

[tex]\frac{x}{(x+2)(x+3)(x+4)} = \frac{x}{x^3 + 9x^2 + 26x + 24}[/tex]

and then just use the product rule and the fact that

[tex]\frac{d}{dx}\frac{1}{f(x)} = -\frac{f^\prime (x)}{\left[f(x)\right]^2}[/tex]
 
  • #7
the4thcafeavenue said:
haha, i guess i'd get mroe help dat way, but, oops hehe
At least, now you've learned your lesson, right? :wink:
 

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function with respect to its independent variable. It can also be thought of as the slope of a curve at a specific point.

Why would someone take a derivative of a "weird" quantity?

Taking a derivative of a "weird" quantity, or a non-standard function, can help in analyzing and understanding its behavior. It can also provide information about the rate of change of the quantity, which can be useful in various applications such as physics, economics, and engineering.

What are some examples of "weird" quantities that can be differentiated?

Some examples of "weird" quantities that can be differentiated include fractals, chaotic systems, and non-analytic functions. These types of functions often exhibit complex behavior and taking their derivatives can provide insight into their dynamics.

How is a derivative calculated?

A derivative can be calculated using various methods, such as the limit definition, the power rule, or the chain rule. The specific method used depends on the form of the function and the desired level of accuracy. In general, the derivative is calculated by finding the slope of a tangent line to the function at a specific point.

What is the significance of taking higher order derivatives?

Taking higher order derivatives, or repeatedly differentiating a function, can provide more information about the behavior of the function. For instance, the second derivative represents the rate of change of the first derivative, and the third derivative represents the rate of change of the second derivative. This information can be useful in analyzing the curvature, concavity, and inflection points of a function.

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