How can I find all the derivatives of the function? [on hold]
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My function is the following
$[f(x)]^2 = e^x int_{1}^{x} t f(t) dt$
While $x epsilon mathbb{R}$
And I need to find all the differentiable functions for f
All I can think of is using the first fundemental theorem in calculus to get rid of the interval.
calculus derivatives
asked yesterday
Nora
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put on hold as off-topic by 5xum, Micah, user10354138, Lee David Chung Lin, Leucippus 11 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Micah, user10354138, Lee David Chung Lin, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
-1
down vote
favorite
My function is the following
$[f(x)]^2 = e^x int_{1}^{x} t f(t) dt$
While $x epsilon mathbb{R}$
And I need to find all the differentiable functions for f
All I can think of is using the first fundemental theorem in calculus to get rid of the interval.
calculus derivatives
asked yesterday
Nora
43
put on hold as off-topic by 5xum, Micah, user10354138, Lee David Chung Lin, Leucippus 11 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Micah, user10354138, Lee David Chung Lin, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
What are you trying to calculate? The derivateives at a given point? Or something else?
– 5xum
yesterday
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
My function is the following
$[f(x)]^2 = e^x int_{1}^{x} t f(t) dt$
While $x epsilon mathbb{R}$
And I need to find all the differentiable functions for f
All I can think of is using the first fundemental theorem in calculus to get rid of the interval.
calculus derivatives
asked yesterday
Nora
43
My function is the following
$[f(x)]^2 = e^x int_{1}^{x} t f(t) dt$
While $x epsilon mathbb{R}$
And I need to find all the differentiable functions for f
All I can think of is using the first fundemental theorem in calculus to get rid of the interval.
calculus derivatives
calculus derivatives
asked yesterday
Nora
43
asked yesterday
Nora
43
edited yesterday
asked yesterday
Nora
43
asked yesterday
Nora
43
asked yesterday
Nora
43
43
put on hold as off-topic by 5xum, Micah, user10354138, Lee David Chung Lin, Leucippus 11 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Micah, user10354138, Lee David Chung Lin, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by 5xum, Micah, user10354138, Lee David Chung Lin, Leucippus 11 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Micah, user10354138, Lee David Chung Lin, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
What are you trying to calculate? The derivateives at a given point? Or something else?
– 5xum
yesterday
add a comment |
What are you trying to calculate? The derivateives at a given point? Or something else?
– 5xum
yesterday
What are you trying to calculate? The derivateives at a given point? Or something else?
– 5xum
yesterday
What are you trying to calculate? The derivateives at a given point? Or something else?
– 5xum
yesterday
add a comment |
1 Answer
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First divide both sides by $e^x$, then differentiate; divide by $f(x)$ (assuming $f$ is not identically $0$), and solve the resulting differential equation with the initial condition $f(1)=0$.
answered yesterday
Robert Israel
312k23206452
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
First divide both sides by $e^x$, then differentiate; divide by $f(x)$ (assuming $f$ is not identically $0$), and solve the resulting differential equation with the initial condition $f(1)=0$.
answered yesterday
Robert Israel
312k23206452
add a comment |
up vote
1
down vote
First divide both sides by $e^x$, then differentiate; divide by $f(x)$ (assuming $f$ is not identically $0$), and solve the resulting differential equation with the initial condition $f(1)=0$.
answered yesterday
Robert Israel
312k23206452
add a comment |
up vote
1
down vote
up vote
1
down vote
First divide both sides by $e^x$, then differentiate; divide by $f(x)$ (assuming $f$ is not identically $0$), and solve the resulting differential equation with the initial condition $f(1)=0$.
answered yesterday
Robert Israel
312k23206452
First divide both sides by $e^x$, then differentiate; divide by $f(x)$ (assuming $f$ is not identically $0$), and solve the resulting differential equation with the initial condition $f(1)=0$.
answered yesterday
Robert Israel
312k23206452
answered yesterday
Robert Israel
312k23206452
answered yesterday
Robert Israel
312k23206452
answered yesterday
Robert Israel
312k23206452
312k23206452
add a comment |
add a comment |
What are you trying to calculate? The derivateives at a given point? Or something else?
– 5xum
yesterday