Is the Quotient Rule Necessary for Finding the Derivative of a Fraction?

In summary, The person is having trouble finding the derivative of the function y=9/x+5 and has tried using the quotient rule and the derivative of (x+5)^-1 * 9, but has encountered problems. They are seeking assistance and have since found their mistake with the quotient rule. The speaker also suggests using the product rule when finding the derivative of a function.
  • #1
Ry122
565
2
Hi
Im trying to find the derivative of y=9/x+5
I tried using the quotient rule and
and the derivative of (x+5)^-1*9 but both methods don't work.
 
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  • #2
If you would show us some work, someone could point out the problem you are having.
 
  • #3
Ry122 said:
Hi
Im trying to find the derivative of y=9/x+5
I tried using the quotient rule and
and the derivative of (x+5)^-1*9 but both methods don't work.

Do you mean y=(9/x)+5 or y=9/(x+5)? From your post, I presume the latter.

As d_leet said, show us your work and we'll guide you.
 
Last edited:
  • #4
its ok i found what i was doing wrong. I made a mistake with the quotient rule. i had u'v+v'u instead of u'v-v'u
 
  • #5
By the way, I'm curious as to why you are using the quotient rule, unless it was a requirement for this problem. Normally the quotient rule is used in the following situation:

[tex]y = \frac{g(x)}{h(x)}[/tex]

In your case, g(x) is a constant and y' can be found directly. Let me ask this. How would you find y' if y = 1/x?

As a side note, I never use the quotient rule, because I can never remember how it works. I always use the product rule:

[tex]y = g(x)h(x)^{-1}[/tex]
 

FAQ: Is the Quotient Rule Necessary for Finding the Derivative of a Fraction?

What is a derivative of a fraction?

A derivative of a fraction is a mathematical concept that represents the rate of change of a function in relation to its input variable. In simpler terms, it is the slope of a curve at a specific point.

How do you find the derivative of a fraction?

To find the derivative of a fraction, you can use the quotient rule or the chain rule, depending on the complexity of the fraction. The quotient rule states that the derivative of a fraction is equal to the denominator multiplied by the derivative of the numerator minus the numerator multiplied by the derivative of the denominator, all divided by the square of the denominator.

What is the purpose of finding the derivative of a fraction?

The purpose of finding the derivative of a fraction is to understand the rate of change of a function. It can help solve real-world problems involving motion, growth, and decay. It also allows us to find the maximum and minimum values of a function.

Can a fraction have a negative derivative?

Yes, a fraction can have a negative derivative. A negative derivative indicates a decreasing function, while a positive derivative indicates an increasing function. The value of the derivative itself does not determine the sign, but rather the direction of the change.

Are there any special cases when finding the derivative of a fraction?

Yes, there are some special cases when finding the derivative of a fraction. One example is when the fraction has a constant in the numerator or denominator. In this case, the derivative is equal to 0. Another case is when the denominator is raised to a power, in which case the power rule can be used.

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