f=f(u,v)
v=v(x,y)=e^x+y
u=u(x,y)=e^x-y
Part of the question I'm working on is asking for df/dv. To work out it's value, is it simply V_xy? Or something like this? (partial of v with respect to x first, then respect to y with the answer?)
v=v(x,y)=e^x+y
u=u(x,y)=e^x-y
Part of the question I'm working on is asking for df/dv. To work out it's value, is it simply V_xy? Or something like this? (partial of v with respect to x first, then respect to y with the answer?)
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You need to know what is f(u,v) first for getting df/dv.- I mean , f(u,v) = v^2+2u^4 , for example , being v=v(x,y)=e^x+y
u=u(x,y)=e^x-y
now, if you want Df/dx
df= (Df/du) du + (df/dv) dv ( total derivative) and
df/dx = (Df/du) (du/dx) + (df/dv) (dv/dx) in the same way
df/dy = (Df/du) (du/dy) + (df/dv) (dv/dy)
Note that you need df/du and df/dv , but for this , you need to know what is f(u,v) .-
u=u(x,y)=e^x-y
now, if you want Df/dx
df= (Df/du) du + (df/dv) dv ( total derivative) and
df/dx = (Df/du) (du/dx) + (df/dv) (dv/dx) in the same way
df/dy = (Df/du) (du/dy) + (df/dv) (dv/dy)
Note that you need df/du and df/dv , but for this , you need to know what is f(u,v) .-
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So what is f(u, v)?? ...in term of u and v... otherwise the partial of f with respect to v is [partial of f(u, v) with respect to v] given that v=v(x,y)=e^x+y and u=u(x,y)=e^x-y. [undoubtedly true, but not too informative]