Differentiating y=f(u) & u=g(x)

[jkeatin]

Homework Statement

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)

Homework Equations

f'(x)=df/dx

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.

 

[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.

 

[jkeatin]

thanks defennder

 

[jkeatin]

wait what does RHS mean?

 

[Saladsamurai]

wait what does RHS mean?

Right hand side

 

[jkeatin]

man, well eventually ill get used to this, thanks

 

[jkeatin]

I really don't understand what's the variables and what's being derived etc

 

[jkeatin]

why do i have to find y''?

 

[Saladsamurai]

man, well eventually ill get used to this, thanks

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.

 

[jkeatin]

cool, thanks casey