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







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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.













  • What are you trying to calculate? The derivateives at a given point? Or something else?
    – 5xum
    yesterday















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







share|cite|improve this 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













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







share|cite|improve this question















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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited yesterday

























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.




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


















  • 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










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 $f(1)=0$.






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    1 Answer
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    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 $f(1)=0$.






    share|cite|improve this answer

























      up vote
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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 $f(1)=0$.






      share|cite|improve this answer























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        up vote
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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 $f(1)=0$.






        share|cite|improve this answer












        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 $f(1)=0$.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered yesterday









        Robert Israel

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