Mixing
chain rule application to multivariate derivative [closed]
Clash Royale CLAN TAG#URR8PPP
up vote
-1
down vote
favorite
I have a book with this in it:
total derivative
But I don't understand where the single quote comes from.
If I look at this: http://tutorial.math.lamar.edu/Classes/CalcIII/ChainRule.aspx
I would assume the total derivative to be:
My take:
with dx/dt being x-dot and dt/dt reducing to 1.
But then I don't have a single quote, which indicates the partial of S with respect to x needs to differentiated with respect to time.
Could someone break down what i'm missing here?
calculus multivariable-calculus derivatives
asked Jul 29 at 10:38
graaf
61
closed as unclear what you're asking by zipirovich, John Ma, Leucippus, Taroccoesbrocco, amWhy Jul 30 at 10:56
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |Â
up vote
-1
down vote
favorite
I have a book with this in it:
total derivative
But I don't understand where the single quote comes from.
If I look at this: http://tutorial.math.lamar.edu/Classes/CalcIII/ChainRule.aspx
I would assume the total derivative to be:
My take:
with dx/dt being x-dot and dt/dt reducing to 1.
But then I don't have a single quote, which indicates the partial of S with respect to x needs to differentiated with respect to time.
Could someone break down what i'm missing here?
calculus multivariable-calculus derivatives
asked Jul 29 at 10:38
graaf
61
closed as unclear what you're asking by zipirovich, John Ma, Leucippus, Taroccoesbrocco, amWhy Jul 30 at 10:56
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
What is $S$? what is $x$? Let's assume that $t$ is a real variable. I'm not sure what's implicit in this notation, can you provide us some more reference?
– Henrique Augusto Souza
Jul 29 at 16:13
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
I have a book with this in it:
total derivative
But I don't understand where the single quote comes from.
If I look at this: http://tutorial.math.lamar.edu/Classes/CalcIII/ChainRule.aspx
I would assume the total derivative to be:
My take:
with dx/dt being x-dot and dt/dt reducing to 1.
But then I don't have a single quote, which indicates the partial of S with respect to x needs to differentiated with respect to time.
Could someone break down what i'm missing here?
calculus multivariable-calculus derivatives
asked Jul 29 at 10:38
graaf
61
I have a book with this in it:
total derivative
But I don't understand where the single quote comes from.
If I look at this: http://tutorial.math.lamar.edu/Classes/CalcIII/ChainRule.aspx
I would assume the total derivative to be:
My take:
with dx/dt being x-dot and dt/dt reducing to 1.
But then I don't have a single quote, which indicates the partial of S with respect to x needs to differentiated with respect to time.
Could someone break down what i'm missing here?
calculus multivariable-calculus derivatives
asked Jul 29 at 10:38
graaf
61
asked Jul 29 at 10:38
graaf
61
asked Jul 29 at 10:38
graaf
61
asked Jul 29 at 10:38
graaf
61
61
closed as unclear what you're asking by zipirovich, John Ma, Leucippus, Taroccoesbrocco, amWhy Jul 30 at 10:56
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by zipirovich, John Ma, Leucippus, Taroccoesbrocco, amWhy Jul 30 at 10:56
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
What is $S$? what is $x$? Let's assume that $t$ is a real variable. I'm not sure what's implicit in this notation, can you provide us some more reference?
– Henrique Augusto Souza
Jul 29 at 16:13
add a comment |Â
1
What is $S$? what is $x$? Let's assume that $t$ is a real variable. I'm not sure what's implicit in this notation, can you provide us some more reference?
– Henrique Augusto Souza
Jul 29 at 16:13
1
1
What is $S$? what is $x$? Let's assume that $t$ is a real variable. I'm not sure what's implicit in this notation, can you provide us some more reference?
– Henrique Augusto Souza
Jul 29 at 16:13
What is $S$? what is $x$? Let's assume that $t$ is a real variable. I'm not sure what's implicit in this notation, can you provide us some more reference?
– Henrique Augusto Souza
Jul 29 at 16:13
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
0
down vote
accepted
It's hard to tell without the context (“I have a book†is useless information – tell us which book it is!), but my guess is that the prime means matrix transposition (like in Matlab, for instance), and that they view the gradient $partial S/partial mathbfx$ as a column vector which must be turned into a row vector in order to be multiplied by the column vector $dotmathbfx$.
answered Jul 29 at 16:42
Hans Lundmark
32.7k563109
the book is 'optimal control systems' by desineni naidu
– graaf
Jul 30 at 6:49
S is the terminal cost part of a functional, so the product should be a scalar. I think you are right, I was too hung up on ' being differentiation to consider the bold face of the x.
– graaf
Jul 30 at 6:59
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
It's hard to tell without the context (“I have a book†is useless information – tell us which book it is!), but my guess is that the prime means matrix transposition (like in Matlab, for instance), and that they view the gradient $partial S/partial mathbfx$ as a column vector which must be turned into a row vector in order to be multiplied by the column vector $dotmathbfx$.
answered Jul 29 at 16:42
Hans Lundmark
32.7k563109
the book is 'optimal control systems' by desineni naidu
– graaf
Jul 30 at 6:49
S is the terminal cost part of a functional, so the product should be a scalar. I think you are right, I was too hung up on ' being differentiation to consider the bold face of the x.
– graaf
Jul 30 at 6:59
add a comment |Â
up vote
0
down vote
accepted
It's hard to tell without the context (“I have a book†is useless information – tell us which book it is!), but my guess is that the prime means matrix transposition (like in Matlab, for instance), and that they view the gradient $partial S/partial mathbfx$ as a column vector which must be turned into a row vector in order to be multiplied by the column vector $dotmathbfx$.
answered Jul 29 at 16:42
Hans Lundmark
32.7k563109
the book is 'optimal control systems' by desineni naidu
– graaf
Jul 30 at 6:49
S is the terminal cost part of a functional, so the product should be a scalar. I think you are right, I was too hung up on ' being differentiation to consider the bold face of the x.
– graaf
Jul 30 at 6:59
add a comment |Â
up vote
0
down vote
accepted
up vote
0
down vote
accepted
It's hard to tell without the context (“I have a book†is useless information – tell us which book it is!), but my guess is that the prime means matrix transposition (like in Matlab, for instance), and that they view the gradient $partial S/partial mathbfx$ as a column vector which must be turned into a row vector in order to be multiplied by the column vector $dotmathbfx$.
answered Jul 29 at 16:42
Hans Lundmark
32.7k563109
It's hard to tell without the context (“I have a book†is useless information – tell us which book it is!), but my guess is that the prime means matrix transposition (like in Matlab, for instance), and that they view the gradient $partial S/partial mathbfx$ as a column vector which must be turned into a row vector in order to be multiplied by the column vector $dotmathbfx$.
answered Jul 29 at 16:42
Hans Lundmark
32.7k563109
answered Jul 29 at 16:42
Hans Lundmark
32.7k563109
answered Jul 29 at 16:42
Hans Lundmark
32.7k563109
answered Jul 29 at 16:42
Hans Lundmark
32.7k563109
32.7k563109
the book is 'optimal control systems' by desineni naidu
– graaf
Jul 30 at 6:49
S is the terminal cost part of a functional, so the product should be a scalar. I think you are right, I was too hung up on ' being differentiation to consider the bold face of the x.
– graaf
Jul 30 at 6:59
add a comment |Â
the book is 'optimal control systems' by desineni naidu
– graaf
Jul 30 at 6:49
S is the terminal cost part of a functional, so the product should be a scalar. I think you are right, I was too hung up on ' being differentiation to consider the bold face of the x.
– graaf
Jul 30 at 6:59
the book is 'optimal control systems' by desineni naidu
– graaf
Jul 30 at 6:49
the book is 'optimal control systems' by desineni naidu
– graaf
Jul 30 at 6:49
S is the terminal cost part of a functional, so the product should be a scalar. I think you are right, I was too hung up on ' being differentiation to consider the bold face of the x.
– graaf
Jul 30 at 6:59
S is the terminal cost part of a functional, so the product should be a scalar. I think you are right, I was too hung up on ' being differentiation to consider the bold face of the x.
– graaf
Jul 30 at 6:59
add a comment |Â
1
What is $S$? what is $x$? Let's assume that $t$ is a real variable. I'm not sure what's implicit in this notation, can you provide us some more reference?
– Henrique Augusto Souza
Jul 29 at 16:13