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y=F(z) where z=x-vt

Now I can find out the value of

[itex] \frac{\partial y}{\partial t} [/itex]

but I don't know how to find out the

[itex] \frac{\partial ^{2} y}{\partial t^{2}} [/itex]

I know that this is equal to

[itex] \frac{d^{2}F}{dz^{2}} (-v)^2 [/itex]

I tried to solve this in this way- just tell me if this is correct

[itex] \frac{ \partial y}{ \partial t}= \frac{dF}{ dz} \frac{ \partial z}{ \partial t}=\frac{dF}{dz} (-v)

\\

\frac{ \partial^{2} y}{ \partial t^{2}}= \frac{\partial }{\partial t} \frac{dF}{dz} (-v)= \frac{d}{dz}\frac{\partial z}{\partial t} \frac{dF}{dz} (-v) = \frac{d^{2}F}{dz^{2}} (-v)^2

[/itex]

Just tell me if the above method is correct

Thanks a lot

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# How to find out [itex]\frac{\partial^{2} y}{\partial t^{2}} [/itex]?

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