More differentiables

1. Jun 29, 2008

jkeatin

1. The problem statement, all variables and given/known data

If y=f(u) and u=g(x)
f and g are differentiable; show that
d^2y/dx^2=d^2y/dx^2(du/dx)^2+dy/du(d^2u/dx^2)

2. Relevant equations
f'(x)=df/dx

3. The attempt at a solution
I think the notation is throwing me off, can this be translated in prime notation? And I know y is a compostion of f and g.

2. Jun 30, 2008

Defennder

You have to apply the product rule to the RHS of dy/dx first when evaluating y'' before applying the chain rule. Doing it the other way round will give you the wrong answer. I did a question like this before, except involving partial derivatives with 3 variables, which made it a hell lot more tedious.

3. Jun 30, 2008

jkeatin

thanks defennder

4. Jun 30, 2008

jkeatin

wait what does RHS mean?

5. Jun 30, 2008

Right hand side

6. Jun 30, 2008

jkeatin

man, well eventually ill get used to this, thanks

7. Jun 30, 2008

jkeatin

I really dont understand whats the variables and whats being derived etc

8. Jun 30, 2008

jkeatin

why do i have to find y''?

9. Jun 30, 2008

It's takes awhile. Keep at it! Don't be afraid tp play around with LaTeX codes too. If you see an image and you want to know how to put it in nice Latex, just click on it and a source code will generate.

Like this:

$$\frac{d^2y}{dx^2}=\frac{d^2y}{dx^2}\cdot(\frac{du}{dx})^2+\frac{dy}{du}\cdot\frac{d^2u}{dx^2}$$

Click on it and see the code that I used to make it.

10. Jun 30, 2008

jkeatin

cool, thanks casey