Mixing
Switching Orders of Differentiation and Integration in case of Function of 2 Variables
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I encountered the following equation in my calculus lecture notes:
$$
frac{d}{dx}int_0^xf(x,y)dy = f(x,x)+int_0^xfrac{partial f}{partial x}(x,y)dy
$$
Could you show me how to prove the above equality?
multivariable-calculus
asked Jan 25 at 17:39
A Slow LearnerA Slow Learner
453213
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add a comment |
$begingroup$
I encountered the following equation in my calculus lecture notes:
$$
frac{d}{dx}int_0^xf(x,y)dy = f(x,x)+int_0^xfrac{partial f}{partial x}(x,y)dy
$$
Could you show me how to prove the above equality?
multivariable-calculus
asked Jan 25 at 17:39
A Slow LearnerA Slow Learner
453213
$endgroup$
add a comment |
$begingroup$
I encountered the following equation in my calculus lecture notes:
$$
frac{d}{dx}int_0^xf(x,y)dy = f(x,x)+int_0^xfrac{partial f}{partial x}(x,y)dy
$$
Could you show me how to prove the above equality?
multivariable-calculus
asked Jan 25 at 17:39
A Slow LearnerA Slow Learner
453213
$endgroup$
I encountered the following equation in my calculus lecture notes:
$$
frac{d}{dx}int_0^xf(x,y)dy = f(x,x)+int_0^xfrac{partial f}{partial x}(x,y)dy
$$
Could you show me how to prove the above equality?
multivariable-calculus
multivariable-calculus
asked Jan 25 at 17:39
A Slow LearnerA Slow Learner
453213
asked Jan 25 at 17:39
A Slow LearnerA Slow Learner
453213
asked Jan 25 at 17:39
A Slow LearnerA Slow Learner
453213
asked Jan 25 at 17:39
A Slow LearnerA Slow Learner
453213
asked Jan 25 at 17:39
A Slow LearnerA Slow Learner
453213
453213
add a comment |
add a comment |
1 Answer
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This is a particular version of what is known as the Leibniz Integral Rule. The wikipedia link provides a nice proof of the general case(s), and it is not too hard to see how this particular form follows
answered Jan 25 at 18:53
Marat AlievMarat Aliev
1312
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add a comment |
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1 Answer
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1 Answer
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$begingroup$
This is a particular version of what is known as the Leibniz Integral Rule. The wikipedia link provides a nice proof of the general case(s), and it is not too hard to see how this particular form follows
answered Jan 25 at 18:53
Marat AlievMarat Aliev
1312
$endgroup$
add a comment |
$begingroup$
This is a particular version of what is known as the Leibniz Integral Rule. The wikipedia link provides a nice proof of the general case(s), and it is not too hard to see how this particular form follows
answered Jan 25 at 18:53
Marat AlievMarat Aliev
1312
$endgroup$
add a comment |
$begingroup$
This is a particular version of what is known as the Leibniz Integral Rule. The wikipedia link provides a nice proof of the general case(s), and it is not too hard to see how this particular form follows
answered Jan 25 at 18:53
Marat AlievMarat Aliev
1312
$endgroup$
This is a particular version of what is known as the Leibniz Integral Rule. The wikipedia link provides a nice proof of the general case(s), and it is not too hard to see how this particular form follows
answered Jan 25 at 18:53
Marat AlievMarat Aliev
1312
answered Jan 25 at 18:53
Marat AlievMarat Aliev
1312
answered Jan 25 at 18:53
Marat AlievMarat Aliev
1312
answered Jan 25 at 18:53
Marat AlievMarat Aliev
1312
1312
add a comment |
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