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\partial{v}=\partial{x} + w\partial{y}

and \partial{w}=x\partial{y}

it seems to me that the first line should read \partial{v}=\partial{x} = w\partial{y}

is this true? i am a bit rusty on multivariable calculus

- Thread starter fishingtreeing
- Start date

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\partial{v}=\partial{x} + w\partial{y}

and \partial{w}=x\partial{y}

it seems to me that the first line should read \partial{v}=\partial{x} = w\partial{y}

is this true? i am a bit rusty on multivariable calculus

- 12,950

- 532

Usually [itex] \partial D[/itex] all by himself means the boundary of the domain D.

Daniel.

- 536

- 1

for this to make any sense, you need to express it as a function, say [itex]f(x,y)[/itex] and then take derivatives of [itex]f[/itex]fishingtreeing said:

\partial{v}=\partial{x} + w\partial{y}

and \partial{w}=x\partial{y}

it seems to me that the first line should read \partial{v}=\partial{x} = w\partial{y}

is this true? i am a bit rusty on multivariable calculus

- 3

- 0

hello, i am supposed to use the two variable chain rule to confirm that changing variables from (x,y) to (v,w) with v=x and w=y/x leads to:

[itex]\frac{\partial}{\partial v} = \frac{\partial}{\partial x} + w\frac{\partial}{\partial y} [/itex]

and [itex]\frac{\partial}{\partial w}=x\frac{\partial}{\partial y}[/itex]

it seems to me that the first line should read [itex]\frac{\partial}{\partial v} = \frac{\partial}{\partial x} = w\frac{\partial}{\partial y} [/itex]

is this true? i am a bit rusty on multivariable calculus

- 12,950

- 532

[tex] \frac{\partial}{\partial v}=\frac{\partial x}{\partial v}\frac{\partial}{\partial x}+

\frac{\partial y}{\partial v}\frac{\partial}{\partial y} [/tex]

[tex] \frac{\partial}{\partial w}=\frac{\partial x}{\partial w}\frac{\partial}{\partial x}+\frac{\partial y}{\partial w}\frac{\partial}{\partial y} [/tex]

There's no other way to apply the chain rule.

You could put it as well in matrix notation using the Jacobian matrix.

Daniel.

- 3

- 0

ok, thanks

i can see where the first one comes from, but if i apply the chain rule to the second one, i get

[itex]\frac{\partial}{\partial w}=\frac{-y}{w^2}\frac{\partial}{\partial x} + x\frac{\partial}{\partial y}[/itex]

is this correct, or is the original correct?

i can see where the first one comes from, but if i apply the chain rule to the second one, i get

[itex]\frac{\partial}{\partial w}=\frac{-y}{w^2}\frac{\partial}{\partial x} + x\frac{\partial}{\partial y}[/itex]

is this correct, or is the original correct?

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