# ∂^2/(∂^2 y)=∂/∂y (ξ_y ∂/∂ξ+η_y ∂/∂η) second derivative problematic

• Dec 30th 2013, 06:49 AM
gorkyerdogan
∂^2/(∂^2 y)=∂/∂y (ξ_y ∂/∂ξ+η_y ∂/∂η) second derivative problematic
Hello guys, I'm pretty new here and I have a problem. I couldn't take 2nd derivative of this equation;

∂^2/(∂^2 y)=∂/∂y (ξ_y ∂/∂ξ+η_y ∂/∂η)

Attachment 29969

• Dec 30th 2013, 08:18 AM
HallsofIvy
Re: ∂^2/(∂^2 y)=∂/∂y (ξ_y ∂/∂ξ+η_y ∂/∂η) second derivative problematic
That's not an equation- you are just saying that those two operators are the same. But I don't understand what it is that you want to take the second derivative of. The second derivative of the left side would be $\displaystyle \frac{\partial^4}{\partial y^4}$ and the second derivative of the right $\displaystyle \frac{\partial^3}{\partial y^3}\left(\xi_y\frac{\partial}{\partial \xi}+ \eta_y\frac{\partial}{\partial \eta}\right)$
but I doubt that is what you are asking.
• Dec 30th 2013, 08:25 AM
gorkyerdogan
Re: ∂^2/(∂^2 y)=∂/∂y (ξ_y ∂/∂ξ+η_y ∂/∂η) second derivative problematic
Attachment 29970

I couldn't expand the right side of the equation by taking 2nd derivative of it. Is it a bit more clear now?
• Dec 30th 2013, 09:15 AM
romsek
Re: ∂^2/(∂^2 y)=∂/∂y (ξ_y ∂/∂ξ+η_y ∂/∂η) second derivative problematic
Quote:

Originally Posted by gorkyerdogan
Attachment 29970

I couldn't expand the right side of the equation by taking 2nd derivative of it. Is it a bit more clear now?

just use the product rule for derivatives

$\displaystyle \frac{\partial}{\partial y}\left(\xi_y \frac{\partial}{\partial \xi}+\eta_y \frac{\partial}{\partial \eta}\right)=\frac{\partial \xi_y}{\partial y}\frac{\partial}{\partial \xi}+\xi_y \frac{\partial}{\partial y \partial \xi}+\frac{\partial \eta_y}{\partial y}\frac{\partial}{\partial \eta}+\eta_y \frac{\partial }{\partial y \partial \eta}$

I hope you understand that these are operators.
• Dec 30th 2013, 10:11 AM
gorkyerdogan
Re: ∂^2/(∂^2 y)=∂/∂y (ξ_y ∂/∂ξ+η_y ∂/∂η) second derivative problematic
Thank you very much mate. This is so helpful for me.