derivatives of quotients

[Laila]

I have a function R(x) = (600 000x - x^2) / 200 000

I have to find the derivative and so far this is where I got:

(600 000 - 2x) / (200 000)^2

I know I'm doing something wrong but I don't know what, and I don't know where to go from here. Can anyone help me?

 

[galactus]

Is this what you mean?

\(\displaystyle \L\\\frac{600000x-x^{2}}{200000}\)

You're misusing the quotient rule.

Try the equivalent:

\(\displaystyle \frac{600000x-x^{2}}{200000}=3x-\frac{x^{2}}{200000}\)

Now, the derivative of 3x is 3

The derivative of \(\displaystyle \frac{x^{2}}{200000}\) is \(\displaystyle \frac{x}{100000}\)

So, you have:

\(\displaystyle \L\\\frac{d}{dx}\left[\frac{600000x-x^{2}}{200000}\right]=3-\frac{x}{100000}\)

 

[Laila]

THANK YOU

 

[Laila]

wait, how did you get the derivative of \(\displaystyle \frac{x^{2}}{200000}\) to be \(\displaystyle \frac{x}{100000}\) ?

 

[stapel]

The tutor applied the Quotient Rule's formula. It might help if you stated what you think that formula is, and how you applied it, so the tutors can help you find your error.

Thank you.

Eliz.

 

[soroban]

Hello, Laila!

I have a function: \(\displaystyle \,R(x) \:= \:\frac{600 000x\,-\,x^2}{200,000}\)

I have to find the derivative.

If the denominator is a constant, we don't need the Quotient Rule.

It can be written: \(\displaystyle \,R(x) \:=\:\frac{1}{200,000}(600,000x\,-\,x^2)\)

Then: \(\displaystyle \,R'(x) \;=\;\frac{1}{200,000}(600,000\,-\,2x) \; =\;\frac{1}{100,000}(300,000\,-\,x)\)


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Note: if the numerator is a constant, we don't need the Quotient Rule.

Example: \(\displaystyle \,y \;= \;\frac{3}{(2x\,-\,5)^6}\)

It can be written: \(\displaystyle \,y \;= \;3(2x\,-\,5)^{-6}\)

Then: \(\displaystyle \,y' \;= \;3(-6)(2x\,-\,5)^{-7}\cdot 2 \;= \;\frac{-36}{(2x\,-\,5)^7}\)
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