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# question on chain rule watch

1. I was doing a few examples was wondering, if I was to d/dx sin(x) it would simply be cos(x).

Why if it was sin(x^-1) would I have to use the chain rule ? Isn't this still just one composite function ?

I was doing this example https://www.youtube.com/watch?v=VxWapdOEUnM and the doing the chain rule on sin(x^-1) is what caught me as I thought it was just cos(x^-1) when using the product rule.
2. (Original post by T-GiuR)
I was doing a few examples was wondering, if I was to d/dx sin(x) it would simply be cos(x).

Why if it was sin(x^-1) would I have to use the chain rule ? Isn't this still just one composite function ?

I was doing this example https://www.youtube.com/watch?v=VxWapdOEUnM and the doing the chain rule on sin(x^-1) is what caught me as I thought it was just cos(x^-1) when using the product rule.
there is no product ....
3. (Original post by TeeEm)
there is no product ....
xSin(x^-1) is a product ?
4. (Original post by T-GiuR)
xSin(x^-1) is a product ?
this is a product but this is not what you wrote in your original question
5. (Original post by T-GiuR)
xSin(x^-1) is a product ?
There was no product in your original post

Could you state what exactly you want to differentiate

Sin(f(x)) will need the chain rule, of course
6. (Original post by T-GiuR)
xSin(x^-1) is a product ?
You didn't write that exact expression in your OP, as is not.

Remember the chain rule.

7. (Original post by tearteto)
sin(X^-1) = 1/sinX
use quotient rule
vdu-udv/V^2
V = sin
u = 1
nice and simple.
This is so horribly wrong my eyes wept at the nice and simple part.
8. (Original post by Phichi)
This is so horribly wrong my eyes wept at the nice and simple part.
sorry, didn't read it properly XD
immediately tried to find the delete button
9. (Original post by TeeEm)
this is a product but this is not what you wrote in your original question
I've confused my self here. Let me try again.

For that question, linked as the youtube video, requires the use of chain rule and product rule for the first expression.

I was under the impression that when I did it, there was no need for the chain rule as I thought sin(x^-1) was just one composite function. The person in the video used the chain rule for sin(x^-1) while using the product rule.

So my question was why did he use the chain rule for sin(x^-1) ? Isn't that just one composite function just the same as sin(x) ?

Hope that makes sense ?
10. (Original post by T-GiuR)
I've confused my self here. Let me try again.

For that question, linked as the youtube video, requires the use of chain rule and product rule for the first expression.

I was under the impression that when I did it, there was no need for the chain rule as I thought sin(x^-1) was just one composite function. The person in the video used the chain rule for sin(x^-1) while using the product rule.

So my question was why did he use the chain rule for sin(x^-1) ? Isn't that just one composite function just the same as sin(x) ?

Hope that makes sense ?
It is good manners to state the question rather than expect people to use a link

What do you mean by "one composite function"?

Sin(1/x) needs the chain rule

Sin(x) is a function and 1/x is a function
11. (Original post by T-GiuR)
I've confused my self here. Let me try again.

For that question, linked as the youtube video, requires the use of chain rule and product rule for the first expression.

I was under the impression that when I did it, there was no need for the chain rule as I thought sin(x^-1) was just one composite function. The person in the video used the chain rule for sin(x^-1) while using the product rule.

So my question was why did he use the chain rule for sin(x^-1) ? Isn't that just one composite function just the same as sin(x) ?

Hope that makes sense ?
this is indeed a composite function.
the chain rule is indeed the rule which deals with composite functions.
It's all about the chain rule, no product.

listen to TenOfThem or PhiChi as they have better typing skills
12. (Original post by Phichi)
You didn't write that exact expression in your OP, as is not.

Remember the chain rule.

So do you use the chain rule for trig expressions like sin(x), cos(x) ect... ?
13. (Original post by T-GiuR)
So do you use the chain rule for trig expressions like sin(x), cos(x) ect... ?
No, you wouldn't need to use the chain rule for .

Use the chain rule for something such as .

The derivative of is well known to be

If you are referring however to the syntax and how to apply it, in the case of , the functions are as follows:

So,
14. (Original post by T-GiuR)
So do you use the chain rule for trig expressions like sin(x), cos(x) ect... ?
Why would you think that

Sin(x) is a single function

Sin(f(x)) is a composite function

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