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# Functions of Several Variables - Differentiation watch

1. Don't have any idea on how to approach this question. Anyone able to lend a hand?
2. (Original post by Sgt.Incontro)

Don't have any idea on how to approach this question. Anyone able to lend a hand?
Just work out the partial derivatives of f; that's the method of approach. And show they satisfy those equations.
3. (Original post by ghostwalker)
Just work out the partial derivatives of f; that's the method of approach. And show they satisfy those equations.
1) How do you work out the partial derivatives?

2) I think that df/dx is a partial derivative, so working out d^2f/dx^2 should be easy. But what about d^2f/dxdy for example? The first part looks trickier.

Thanks for the help.
4. (Original post by Sgt.Incontro)
1) How do you work out the partial derivatives?
To work out a partial derivative wrt x say, you treat all the other variables as constants, and in effect differentiate as normal.

2) I think that df/dx is a partial derivative, so working out d^2f/dx^2 should be easy. But what about d^2f/dxdy for example? The first part looks trickier.

Thanks for the help.

So, in this case, take the partial derivative wrt y first, and taking the result of that, take the partial derivative wrt x.
5. (Original post by ghostwalker)
To work out a partial derivative wrt x say, you treat all the other variables as constants, and in effect differentiate as normal.

So, in this case, take the partial derivative wrt y first, and taking the result of that, take the partial derivative wrt x.
Makes a lot more sense now, thanks a lot!
6. (Original post by Sgt.Incontro)
Makes a lot more sense now, thanks a lot!
Good.

You're welcome.
7. (Original post by ghostwalker)
x
So what would the partial derivatives be in this case? I.e df/dx and df/dy?

Am I right in thinking that this is NOT like implicit differentiation?

so df/dx = e^x(cos(y))
df/dy = -e^x(sin(y)) ?
8. (Original post by Sgt.Incontro)
So what would the partial derivatives be in this case? I.e df/dx and df/dy?

Am I right in thinking that this is NOT like implicit differentiation?

so df/dx = e^x(cos(y))
df/dy = -e^x(sin(y)) ?
Yes, it's not like implicit differentiation. More like standard differentiation.

And those are correct.

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