2nd order partial derivative

[tekzou]

Hi all,

I had that weird problem on my monday course.

I need to find the second derivative of a function. f=(x^2+y^2)/2 where x=g(u,v) and y=h(u)

The only thing is that I only have a contour map of the function g(u,v).

I can easily approximate the first partial derivative df/dv where df/dx * dx/dv but how do I do d²f/dv² ? :?

Thanks for the help !

 

[Deleted member 4993]

Hi all,

I had that weird problem on my monday course.

I need to find the second derivative of a function. f=(x^2+y^2)/2 where x=g(u,v) and y=h(u)

The only thing is that I ony have a contour map of the function g(u,v).

I can easily approximate the first partial derivative df/dv where df/dx * dx/dv but how do I do d²f/dv² ? :?

Thanks for the help !

d/dv (df/dv) = d/dv[df/dx * dx/dv]



Now use chain rule....

 

[tekzou]

d/dv (df/dv) = d/dv[df/dx * dx/dv]


Now use chain rule....

Thanks for the answer. I know about the chain rule but I can't seem to get how to apply it on my case.

If I understood correctly :

df/dx = x
dx/dv = g(u,v+h) - g(u,v) / h <----- approximation I can get with my contour map

d/dv[df/dx * dx/dv] = x * d/dv[g(u,v+h) - g(u,v) / h] = x * g(u,v+2h) - g(u,v) / 2h ?