Hard Calculus Question

[amberzak]

Hi.

I'm currently doing a very intensive maths course, and I am doing calculus (which I am really enjoying). But there is a question that my teacher warned is quite tricky.

If x = 5t^2 and y = 10t, find dy/dx and d^2y/dx^2 in terms of t.

I think it might have something to do with the chain rule maybe? Any clue where to start?

Thanks

 

[daon2]

Hi.

I'm currently doing a very intensive maths course, and I am doing calculus (which I am really enjoying). But there is a question that my teacher warned is quite tricky.

If x = 5t^2 and y = 10t, find dy/dx and d^2y/dx^2 in terms of t.

I think it might have something to do with the chain rule maybe? Any clue where to start?

Thanks

\(\displaystyle \frac{dy}{dx} = \frac{d}{dx}(y) = \frac{dy}{dt} / \frac{dx}{dt} \)

Now for the second derivative, instead of your function being 'y' it is 'dy/dx', so apply the formula above to dy/dx:

\(\displaystyle \frac{d^2y}{dx^2} = \frac{d}{dx}\left(\frac{dy}{dx}\right) \)

 

[amberzak]

Ah, got it.
Thanks