(Solved) Find the derivative by using the quotient rule.

slimes

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3 years ago Edited: 3 years ago, slimes

Find the derivative by using the quotient rule.

Need help with question1.
I've showed my work for 2. so would that be the correct answer?

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bio_man

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3 years ago

Please watch the following two videos on this topic:

I'll answer soon...

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bio_man

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Educator

3 years ago

Hi slimes

My best piece of advice is to ignore the "quotient rule" altogether and use the product rule instead.

For example, you function is:

\(q\left(x\right)=\frac{x+3}{\sqrt{x^2-1}}\)

Rewrite it according to the laws of exponents like this:

\(q\left(x\right)=\frac{x+3}{\sqrt{x^2-1}}\rightarrow \frac{x+3}{\left(x^2-1\right)^{\frac{1}{2}}}\rightarrow \left(x+3\right)\left(x^2-1\right)^{-\frac{1}{2}}\)

\(q\left(x\right)=\left(x+3\right)\left(x^2-1\right)^{-\frac{1}{2}}\)

I think it's just easier to find the derivative of the highlighted function using the product rule instead. The quotient rule (IMO) is a made up rule for students who don't know how to work with exponents.

What do you think?

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bio_man

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bio_man

wrote...

Educator

3 years ago

#2

What you see in blue is the simplest it can go.

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slimes Author

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3 years ago

Hey bio_man thank you so much Smiling Face with Open Mouth

Quote from: bio_man (3 years ago)

Hi slimes My best piece of advice is to ignore the "quotient rule" altogether and use the product rule instead. For example, you function is: \(q\left(x\right)=\frac{x+3}{\sqrt{x^2-1}}\) Rewrite it according to the laws of exponents like this: \(q\left(x\right)=\frac{x+3}{\sqrt{x^2-1}}\rightarrow \frac{x+3}{\left(x^2-1\right)^{\frac{1}{2}}}\rightarrow \left(x+3\right)\left(x^2-1\right)^{-\frac{1}{2}}\) \(q\left(x\right)=\left(x+3\right)\left(x^2-1\right)^{-\frac{1}{2}}\) I think it's just easier to find the derivative of the highlighted function using the product rule instead. The quotient rule (IMO) is a made up rule for students who don't know how to work with exponents. What do you think?

I agree this would be a lot easier to use the product rule, but then I wouldn't really using the "quotient rule" because it is kind of the whole point of the lesson, but I could ask if I can still do that.

Quote from: bio_man (3 years ago)

We don't need to simplify further, so up to green is good!
Also did you just use the chain rule to find the derivative of the denominator/v which is x/√x^2 - 1 and then combined it with -(x + 3) to get the final answer?

Quote from: bio_man (3 years ago)

#2 What you see in blue is the simplest it can go.

So would my answer still be correct then without simplifying it?

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bio_man

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Educator

3 years ago

Quote from: slimes (3 years ago)

My opinion is that you can perform all derivatives without ever knowing the "quotient rule"; in fact, only in high schools have I seen this "rule" be implemented. But as they say, when in Rome, do as the Roman's do, so let's just play according to their rules.

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We don't need to simplify further, so up to green is good!

Really? That's so easy then...

Quote

Also did you just use the chain rule to find the derivative of the denominator/v which is x/√x^2 - 1 and then combined it with -(x + 3) to get the final answer?

Not sure what you're asking, I did the quotient rule and all my steps were shown.

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So would my answer still be correct then without simplifying it?

Really depends on your teacher. Why not show they my work (written obviously by you) and ask them at which step they are MOST okay with.

Let me know...

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slimes Author

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3 years ago

Really? That's so easy then...

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Also did you just use the chain rule to find the derivative of the denominator/v which is x/√x^2 - 1 and then combined it with -(x + 3) to get the final answer?

Yeah my teacher said it isn't really necessary to simplify, in university they would want you to, like simplify the whole thing.

Not sure what you're asking, I did the quotient rule and all my steps were shown.

Quote

So would my answer still be correct then without simplifying it?

I just wanted to clarify that you got this part of your answer by green, by finding the derivative of v, and then combined it with -(x + 3).

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slimes Author

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3 years ago

Really depends on your teacher. Why not show they my work (written obviously by you) and ask them at which step they are MOST okay with. Let me know... [/quote]
In yellow, would be considered the right answer according to my teacher.
Would this mean that the answer that I did is incorrect?

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bio_man

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Educator

3 years ago

Quote from: slimes (3 years ago)

Really depends on your teacher. Why not show they my work (written obviously by you) and ask them at which step they are MOST okay with. Let me know...

In yellow, would be considered the right answer according to my teacher. Would this mean that the answer that I did is incorrect? [/quote]

The answer you wrote is not incorrect, just not simplified enough.

Also, in reference to your other questions, I hope my attachment clarifies what's up

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slimes Author

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#10

3 years ago

Hey I was right Slight Smile

thank you again bio_man

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bio_man

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#11

Educator

3 years ago

Happy to help, make sure to watch and like the videos I shared earlier.

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slimes Author

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#12

3 years ago Edited: 3 years ago, slimes

sure but I don't have a google/youtube account but I will create a random one just so I can like the videos Smiling Face with Open Mouth

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bio_man

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#13

Educator

3 years ago

Appreciate that... but why don't you have a Google account?

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