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

[Ry122]

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.

 

[d_leet]

If you would show us some work, someone could point out the problem you are having.

 

[hotvette]

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.

 

[Ry122]

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

 

[hotvette]

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:

$$y = \frac{g(x)}{h(x)}$$

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:

$$y = g(x)h(x)^{-1}$$