Mixing
How to anti-derivative the partial derivative of a multivariate function across all variables to end up with...
$begingroup$
Partial differentiation of the function
$$y=hat{y} exp{left(-sum^n_{i=1}frac{alpha_i}{x_i}right)}$$
with respect to $x_i$ gives
$$frac{partial y}{partial x_i}=yfrac{alpha_i}{x_i^2}$$
which can be rearranged
$$frac{partial ln y}{partial ln x_i}=alpha_ifrac{d ln x_i}{dx_i}$$
(You see physicists doing this sort of thing anyway.)
How can I reverse this process to start with the last equation and end up with the first? If you have major objections to the rearrangement in the third equation, then how can I start with the second equation and end up with the first?
calculus integration exponential-function partial-derivative
asked Jan 14 at 13:22
benben
95111129
$endgroup$
add a comment |
$begingroup$
Partial differentiation of the function
$$y=hat{y} exp{left(-sum^n_{i=1}frac{alpha_i}{x_i}right)}$$
with respect to $x_i$ gives
$$frac{partial y}{partial x_i}=yfrac{alpha_i}{x_i^2}$$
which can be rearranged
$$frac{partial ln y}{partial ln x_i}=alpha_ifrac{d ln x_i}{dx_i}$$
(You see physicists doing this sort of thing anyway.)
How can I reverse this process to start with the last equation and end up with the first? If you have major objections to the rearrangement in the third equation, then how can I start with the second equation and end up with the first?
calculus integration exponential-function partial-derivative
asked Jan 14 at 13:22
benben
95111129
$endgroup$
add a comment |
$begingroup$
Partial differentiation of the function
$$y=hat{y} exp{left(-sum^n_{i=1}frac{alpha_i}{x_i}right)}$$
with respect to $x_i$ gives
$$frac{partial y}{partial x_i}=yfrac{alpha_i}{x_i^2}$$
which can be rearranged
$$frac{partial ln y}{partial ln x_i}=alpha_ifrac{d ln x_i}{dx_i}$$
(You see physicists doing this sort of thing anyway.)
How can I reverse this process to start with the last equation and end up with the first? If you have major objections to the rearrangement in the third equation, then how can I start with the second equation and end up with the first?
calculus integration exponential-function partial-derivative
asked Jan 14 at 13:22
benben
95111129
$endgroup$
Partial differentiation of the function
$$y=hat{y} exp{left(-sum^n_{i=1}frac{alpha_i}{x_i}right)}$$
with respect to $x_i$ gives
$$frac{partial y}{partial x_i}=yfrac{alpha_i}{x_i^2}$$
which can be rearranged
$$frac{partial ln y}{partial ln x_i}=alpha_ifrac{d ln x_i}{dx_i}$$
(You see physicists doing this sort of thing anyway.)
How can I reverse this process to start with the last equation and end up with the first? If you have major objections to the rearrangement in the third equation, then how can I start with the second equation and end up with the first?
calculus integration exponential-function partial-derivative
calculus integration exponential-function partial-derivative
asked Jan 14 at 13:22
benben
95111129
asked Jan 14 at 13:22
benben
95111129
asked Jan 14 at 13:22
benben
95111129
asked Jan 14 at 13:22
benben
95111129
asked Jan 14 at 13:22
benben
95111129
95111129
add a comment |
add a comment |
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