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

slimes

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3 years ago

Find the derivative by using the chain rule.

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bio_man

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3 years ago

Hi slimes

Welcome back. Currently at the gym, so please watch this video to help you understand the chain rule. It's one of the most important things when deriving.

First video is v. important, also don't forget to give it a like 👍

https://youtube.com/watch?v=jSkDFR3ZR-k

https://youtube.com/watch?v=iei5Kuc2wLg

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bio_man

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slimes Author

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3 years ago

Hi bio_man, thank you so much and just to clarify, to get -x on the side of (4-x^2)^-1/2, you multiplied the left over 1 that you canceled out from the 1/2 in the front and multiplied it to the -x, from the canceled out 2 of (-2x).

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bio_man

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3 years ago

Yes. At this point, you can rearrange the factors a little bit:

\(f\left(x\right)=\frac{1}{2}\left(4-x^2\right)^{-\frac{1}{2}}\left(-2x\right)\)

Rearrange to:

\(f\left(x\right)=\frac{1}{2}\left(-2x\right)\left(4-x^2\right)^{-\frac{1}{2}}\)

You can see it clearer here, how the two factors at the front multiply and cancel out in the process.

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slimes Author

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3 years ago

thank you so much Slight Smile

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slimes Author

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3 years ago

Hey bio_man I have another question. What if there was a question that was sort of similar to this but for that part,

Quote from: bio_man (3 years ago)

Yes. At this point, you can rearrange the factors a little bit: \(f\left(x\right)=\frac{1}{2}\left(4-x^2\right)^{-\frac{1}{2}}\left(-2x\right)\) Rearrange to: \(f\left(x\right)=\frac{1}{2}\left(-2x\right)\left(4-x^2\right)^{-\frac{1}{2}}\) You can see it clearer here, how the two factors at the front multiply and cancel out in the process.

there is nothing to cancel out, would you still have to multiply?
Here is the question I'm talking about, because when I did that it was wrong.

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bio_man

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3 years ago

This part is no good. If you distribute the 1/2 into the parentheses, you have to keep it within its parentheses. Also, try not to use decimals.

\(\left(1-\frac{15}{2}x^4\right)\left(2x-3x^5\right)^{-\frac{1}{2}}\)

*Notice how the first factor is kept inside parentheses

\(\frac{1-\frac{15}{2}x^4}{\sqrt{2x-3x^5}}\)

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slimes Author

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3 years ago

Hey, thanks again just fixed it and got the same answer. My teacher had wrote the answer like this:
I want to confirm, would it still be considered the same?

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bio_man

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3 years ago

Yeah, so what your teacher did was leave the 1/2 as a factor in the numerator, then he/she took it one step further and wrote it as a factor of the entire fraction, which is allowed.

However, be mindful that my interpretation is 100% correct, and you should get full marks for it Slight Smile

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slimes Author

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#10

3 years ago

thank you!

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