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# FP2 Differentiation (Chain rule)

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1. Hi,

The chain rule is: dy/dx = dy/dv * dv/dx
So why in this question does it differentiate dv/dx to be d2v/dx2 . Where does the dy/dv go? Picture is attached.
2. (Original post by Seytonic)
Hi,

The chain rule is: dy/dx = dy/dv * dv/dx
So why in this question does it differentiate dv/dx to be d2v/dx2 . Where does the dy/dv go? Picture is attached.
I'm not quite sure how you're applying the chain rule there.

We have dy/dx = x(dv/dx) + v
Then d^2y/dx^2 is just the derivative of that with respect to x.

By the chain rule, the derivative of x(dv/dx) with respect to x is 1*(dv/dx) + x*(d^2v/dx^2) and of course the derivative of v with respect to x is just dv/dx. And you add them for the mark scheme answer
3. (Original post by Seytonic)
Hi,

The chain rule is: dy/dx = dy/dv * dv/dx
So why in this question does it differentiate dv/dx to be d2v/dx2 . Where does the dy/dv go? Picture is attached.
You don't need the chain rule here.

Differentiate both sides with respect to x using the product rule for the first term.

And use the fact that

4. (Original post by 13 1 20 8 42)
I'm not quite sure how you're applying the chain rule there.

We have dy/dx = x(dv/dx) + v
Then d^2y/dx^2 is just the derivative of that with respect to x.

By the chain rule, the derivative of x(dv/dx) with respect to x is 1*(dv/dx) + x*(d^2v/dx^2) and of course the derivative of v with respect to x is just dv/dx. And you add them for the mark scheme answer
(Original post by notnek)
You don't need the chain rule here.

Differentiate both sides with respect to x using the product rule for the first term.

And use the fact that

Thanks for your responses, I think I see where you're coming from, but why in this other question (which I got right) did my approach work? Pic is attached.
EDIT: For the 2nd blue circle I meant to highlight dt/tx

5. (Original post by Seytonic)
Thanks for your responses, I think I see where you're coming from, but why in this other question (which I got right) did my approach work? Pic is attached.
Sorry I meant product rule before. That approach is right because in that case chain rule is needed
6. (Original post by Seytonic)
Thanks for your responses, I think I see where you're coming from, but why in this other question (which I got right) did my approach work? Pic is attached.
EDIT: For the 2nd blue circle I meant to highlight dt/tx

In this case you have a derivative with respect to on the right-hand-side so if you want to differentiate the whole thing with respect to x then you need the chain rule.

In the previous question every derivative was respect to x so you can differentiate without the chain rule.
7. (Original post by notnek)
In this case you have a derivative with respect to on the right-hand-side so if you want to differentiate the whole thing with respect to x then you need the chain rule.

In the previous question every derivative was respect to x so you can differentiate without the chain rule.
Ahhh, that clears it up, cheers.

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