Alternative Higher Order Partial Derivative Notation
We have that for a bivariate function $f(x,y)$,
$$frac{partial f}{partial x}=f_x(x,y)$$
$$frac{partial^2 f}{partial x^2}=f_{xx}(x,y)$$
$$frac{partial^3 f}{partial x^3}=f_{xxx}(x,y)$$
So for a single variable function, for a derivative involving the "prime" notation, we have that
$$frac{d^n}{dx^n}=f^{(n)}(x)=f''^{...text{n times}}(x)$$
So instead of writing the "prime" 15 times for a 15th derivative, the notation allows us to shorten this. Is there a similar notation for higher order partial derivatives? Like,
$$frac{partial^n f}{partial x^n}=f_{x^{(n)}}(x,y)$$
multivariable-calculus partial-derivative
asked Dec 26 at 15:04
Eleven-Eleven
5,39072659
add a comment |
We have that for a bivariate function $f(x,y)$,
$$frac{partial f}{partial x}=f_x(x,y)$$
$$frac{partial^2 f}{partial x^2}=f_{xx}(x,y)$$
$$frac{partial^3 f}{partial x^3}=f_{xxx}(x,y)$$
So for a single variable function, for a derivative involving the "prime" notation, we have that
$$frac{d^n}{dx^n}=f^{(n)}(x)=f''^{...text{n times}}(x)$$
So instead of writing the "prime" 15 times for a 15th derivative, the notation allows us to shorten this. Is there a similar notation for higher order partial derivatives? Like,
$$frac{partial^n f}{partial x^n}=f_{x^{(n)}}(x,y)$$
multivariable-calculus partial-derivative
asked Dec 26 at 15:04
Eleven-Eleven
5,39072659
2
Try this ... en.wikipedia.org/wiki/Multi-index_notation
– GEdgar
Dec 26 at 15:08
add a comment |
We have that for a bivariate function $f(x,y)$,
$$frac{partial f}{partial x}=f_x(x,y)$$
$$frac{partial^2 f}{partial x^2}=f_{xx}(x,y)$$
$$frac{partial^3 f}{partial x^3}=f_{xxx}(x,y)$$
So for a single variable function, for a derivative involving the "prime" notation, we have that
$$frac{d^n}{dx^n}=f^{(n)}(x)=f''^{...text{n times}}(x)$$
So instead of writing the "prime" 15 times for a 15th derivative, the notation allows us to shorten this. Is there a similar notation for higher order partial derivatives? Like,
$$frac{partial^n f}{partial x^n}=f_{x^{(n)}}(x,y)$$
multivariable-calculus partial-derivative
asked Dec 26 at 15:04
Eleven-Eleven
5,39072659
We have that for a bivariate function $f(x,y)$,
$$frac{partial f}{partial x}=f_x(x,y)$$
$$frac{partial^2 f}{partial x^2}=f_{xx}(x,y)$$
$$frac{partial^3 f}{partial x^3}=f_{xxx}(x,y)$$
So for a single variable function, for a derivative involving the "prime" notation, we have that
$$frac{d^n}{dx^n}=f^{(n)}(x)=f''^{...text{n times}}(x)$$
So instead of writing the "prime" 15 times for a 15th derivative, the notation allows us to shorten this. Is there a similar notation for higher order partial derivatives? Like,
$$frac{partial^n f}{partial x^n}=f_{x^{(n)}}(x,y)$$
multivariable-calculus partial-derivative
multivariable-calculus partial-derivative
asked Dec 26 at 15:04
Eleven-Eleven
5,39072659
asked Dec 26 at 15:04
Eleven-Eleven
5,39072659
asked Dec 26 at 15:04
Eleven-Eleven
5,39072659
asked Dec 26 at 15:04
Eleven-Eleven
5,39072659
asked Dec 26 at 15:04
Eleven-Eleven
5,39072659
5,39072659
2
Try this ... en.wikipedia.org/wiki/Multi-index_notation
– GEdgar
Dec 26 at 15:08
add a comment |
2
Try this ... en.wikipedia.org/wiki/Multi-index_notation
– GEdgar
Dec 26 at 15:08
2
2
Try this ... en.wikipedia.org/wiki/Multi-index_notation
– GEdgar
Dec 26 at 15:08
Try this ... en.wikipedia.org/wiki/Multi-index_notation
– GEdgar
Dec 26 at 15:08
add a comment |
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Try this ... en.wikipedia.org/wiki/Multi-index_notation
– GEdgar
Dec 26 at 15:08