Given d/dx (f(x)) = sqrt f(x), find d/dx ( sqrt f(x)). [closed]

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I am studying for a Calculus test and practicing questions in my Stewart textbook. I came across this question and it seemed too simple. However, it might just be that. My work is shown below thanks in advance for providing any feedback. I was wondering if what I wrote was correct, but I worked through it with somebody in the comment section.



sqrt x = 1 / 2 sqrt x



sqrt f(x) = 1 / 2 sqrt f(x)




calculus derivatives implicit-differentiation




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closed as unclear what you're asking by John Ma, Taroccoesbrocco, Marcus M, Mostafa Ayaz, Aloizio Macedo♦ Jul 21 at 20:46


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.










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    Welcome to the site! Here's a guide to MathJax, which makes symbols and equations look neater.
    – Toby Mak
    Jul 21 at 3:33














up vote
-2
down vote

favorite
1












I am studying for a Calculus test and practicing questions in my Stewart textbook. I came across this question and it seemed too simple. However, it might just be that. My work is shown below thanks in advance for providing any feedback. I was wondering if what I wrote was correct, but I worked through it with somebody in the comment section.



sqrt x = 1 / 2 sqrt x



sqrt f(x) = 1 / 2 sqrt f(x)




calculus derivatives implicit-differentiation




share|cite|improve this question













closed as unclear what you're asking by John Ma, Taroccoesbrocco, Marcus M, Mostafa Ayaz, Aloizio Macedo♦ Jul 21 at 20:46


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




    Welcome to the site! Here's a guide to MathJax, which makes symbols and equations look neater.
    – Toby Mak
    Jul 21 at 3:33












up vote
-2
down vote

favorite
1









up vote
-2
down vote

favorite
1






1





I am studying for a Calculus test and practicing questions in my Stewart textbook. I came across this question and it seemed too simple. However, it might just be that. My work is shown below thanks in advance for providing any feedback. I was wondering if what I wrote was correct, but I worked through it with somebody in the comment section.



sqrt x = 1 / 2 sqrt x



sqrt f(x) = 1 / 2 sqrt f(x)




calculus derivatives implicit-differentiation




share|cite|improve this question













I am studying for a Calculus test and practicing questions in my Stewart textbook. I came across this question and it seemed too simple. However, it might just be that. My work is shown below thanks in advance for providing any feedback. I was wondering if what I wrote was correct, but I worked through it with somebody in the comment section.



sqrt x = 1 / 2 sqrt x



sqrt f(x) = 1 / 2 sqrt f(x)





calculus derivatives implicit-differentiation





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 24 at 22:19
























asked Jul 21 at 3:31









carter

15




15




closed as unclear what you're asking by John Ma, Taroccoesbrocco, Marcus M, Mostafa Ayaz, Aloizio Macedo♦ Jul 21 at 20:46


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 John Ma, Taroccoesbrocco, Marcus M, Mostafa Ayaz, Aloizio Macedo♦ Jul 21 at 20:46


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




    Welcome to the site! Here's a guide to MathJax, which makes symbols and equations look neater.
    – Toby Mak
    Jul 21 at 3:33












  • 1




    Welcome to the site! Here's a guide to MathJax, which makes symbols and equations look neater.
    – Toby Mak
    Jul 21 at 3:33







1




1




Welcome to the site! Here's a guide to MathJax, which makes symbols and equations look neater.
– Toby Mak
Jul 21 at 3:33




Welcome to the site! Here's a guide to MathJax, which makes symbols and equations look neater.
– Toby Mak
Jul 21 at 3:33










1 Answer
1






active

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up vote
2
down vote













Do not omit typing $fracddx$. Omitting those means a completely different thing.



$$colorredfracddxsqrtx=frac12sqrtx$$



and for the problem, you have to use the chain rule.



$$colorredfracddxsqrtf(x)=frac12sqrtf(x)colorredfracddxf(x).$$



We can further simplify the expression using the information that is given.



Edit:



Try to complete the following:



$$frac12sqrtf(x)fracddxf(x)=frac12sqrtf(x)cdotsqrtf(x)=?$$






share|cite|improve this answer























  • Okay for omitting d/dx in my work. To simplify even more the derivative of f(x) would be f(1)
    – carter
    Jul 21 at 3:44










  • hmm... how do you obtain $f(1)$?
    – Siong Thye Goh
    Jul 21 at 3:45










  • Are we trying to find the derivative for f(x) by simplifying the answer? The derivative of f(x) is f(1) because the derivative of x is 1 by the power rule.
    – carter
    Jul 21 at 3:48










  • So suppose $f(x)=x^3$, are you claiming that derivative of $f$ is constant everywhere?
    – Siong Thye Goh
    Jul 21 at 3:51










  • x^3 = 3x^2. Would f go away and all there would be is 1?
    – carter
    Jul 21 at 3:52

















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
2
down vote













Do not omit typing $fracddx$. Omitting those means a completely different thing.



$$colorredfracddxsqrtx=frac12sqrtx$$



and for the problem, you have to use the chain rule.



$$colorredfracddxsqrtf(x)=frac12sqrtf(x)colorredfracddxf(x).$$



We can further simplify the expression using the information that is given.



Edit:



Try to complete the following:



$$frac12sqrtf(x)fracddxf(x)=frac12sqrtf(x)cdotsqrtf(x)=?$$






share|cite|improve this answer























  • Okay for omitting d/dx in my work. To simplify even more the derivative of f(x) would be f(1)
    – carter
    Jul 21 at 3:44










  • hmm... how do you obtain $f(1)$?
    – Siong Thye Goh
    Jul 21 at 3:45










  • Are we trying to find the derivative for f(x) by simplifying the answer? The derivative of f(x) is f(1) because the derivative of x is 1 by the power rule.
    – carter
    Jul 21 at 3:48










  • So suppose $f(x)=x^3$, are you claiming that derivative of $f$ is constant everywhere?
    – Siong Thye Goh
    Jul 21 at 3:51










  • x^3 = 3x^2. Would f go away and all there would be is 1?
    – carter
    Jul 21 at 3:52














up vote
2
down vote













Do not omit typing $fracddx$. Omitting those means a completely different thing.



$$colorredfracddxsqrtx=frac12sqrtx$$



and for the problem, you have to use the chain rule.



$$colorredfracddxsqrtf(x)=frac12sqrtf(x)colorredfracddxf(x).$$



We can further simplify the expression using the information that is given.



Edit:



Try to complete the following:



$$frac12sqrtf(x)fracddxf(x)=frac12sqrtf(x)cdotsqrtf(x)=?$$






share|cite|improve this answer























  • Okay for omitting d/dx in my work. To simplify even more the derivative of f(x) would be f(1)
    – carter
    Jul 21 at 3:44










  • hmm... how do you obtain $f(1)$?
    – Siong Thye Goh
    Jul 21 at 3:45










  • Are we trying to find the derivative for f(x) by simplifying the answer? The derivative of f(x) is f(1) because the derivative of x is 1 by the power rule.
    – carter
    Jul 21 at 3:48










  • So suppose $f(x)=x^3$, are you claiming that derivative of $f$ is constant everywhere?
    – Siong Thye Goh
    Jul 21 at 3:51










  • x^3 = 3x^2. Would f go away and all there would be is 1?
    – carter
    Jul 21 at 3:52












up vote
2
down vote










up vote
2
down vote









Do not omit typing $fracddx$. Omitting those means a completely different thing.



$$colorredfracddxsqrtx=frac12sqrtx$$



and for the problem, you have to use the chain rule.



$$colorredfracddxsqrtf(x)=frac12sqrtf(x)colorredfracddxf(x).$$



We can further simplify the expression using the information that is given.



Edit:



Try to complete the following:



$$frac12sqrtf(x)fracddxf(x)=frac12sqrtf(x)cdotsqrtf(x)=?$$






share|cite|improve this answer















Do not omit typing $fracddx$. Omitting those means a completely different thing.



$$colorredfracddxsqrtx=frac12sqrtx$$



and for the problem, you have to use the chain rule.



$$colorredfracddxsqrtf(x)=frac12sqrtf(x)colorredfracddxf(x).$$



We can further simplify the expression using the information that is given.



Edit:



Try to complete the following:



$$frac12sqrtf(x)fracddxf(x)=frac12sqrtf(x)cdotsqrtf(x)=?$$







share|cite|improve this answer















share|cite|improve this answer



share|cite|improve this answer








edited Jul 21 at 4:24


























answered Jul 21 at 3:39









Siong Thye Goh

77.6k134795




77.6k134795











  • Okay for omitting d/dx in my work. To simplify even more the derivative of f(x) would be f(1)
    – carter
    Jul 21 at 3:44










  • hmm... how do you obtain $f(1)$?
    – Siong Thye Goh
    Jul 21 at 3:45










  • Are we trying to find the derivative for f(x) by simplifying the answer? The derivative of f(x) is f(1) because the derivative of x is 1 by the power rule.
    – carter
    Jul 21 at 3:48










  • So suppose $f(x)=x^3$, are you claiming that derivative of $f$ is constant everywhere?
    – Siong Thye Goh
    Jul 21 at 3:51










  • x^3 = 3x^2. Would f go away and all there would be is 1?
    – carter
    Jul 21 at 3:52
















  • Okay for omitting d/dx in my work. To simplify even more the derivative of f(x) would be f(1)
    – carter
    Jul 21 at 3:44










  • hmm... how do you obtain $f(1)$?
    – Siong Thye Goh
    Jul 21 at 3:45










  • Are we trying to find the derivative for f(x) by simplifying the answer? The derivative of f(x) is f(1) because the derivative of x is 1 by the power rule.
    – carter
    Jul 21 at 3:48










  • So suppose $f(x)=x^3$, are you claiming that derivative of $f$ is constant everywhere?
    – Siong Thye Goh
    Jul 21 at 3:51










  • x^3 = 3x^2. Would f go away and all there would be is 1?
    – carter
    Jul 21 at 3:52















Okay for omitting d/dx in my work. To simplify even more the derivative of f(x) would be f(1)
– carter
Jul 21 at 3:44




Okay for omitting d/dx in my work. To simplify even more the derivative of f(x) would be f(1)
– carter
Jul 21 at 3:44












hmm... how do you obtain $f(1)$?
– Siong Thye Goh
Jul 21 at 3:45




hmm... how do you obtain $f(1)$?
– Siong Thye Goh
Jul 21 at 3:45












Are we trying to find the derivative for f(x) by simplifying the answer? The derivative of f(x) is f(1) because the derivative of x is 1 by the power rule.
– carter
Jul 21 at 3:48




Are we trying to find the derivative for f(x) by simplifying the answer? The derivative of f(x) is f(1) because the derivative of x is 1 by the power rule.
– carter
Jul 21 at 3:48












So suppose $f(x)=x^3$, are you claiming that derivative of $f$ is constant everywhere?
– Siong Thye Goh
Jul 21 at 3:51




So suppose $f(x)=x^3$, are you claiming that derivative of $f$ is constant everywhere?
– Siong Thye Goh
Jul 21 at 3:51












x^3 = 3x^2. Would f go away and all there would be is 1?
– carter
Jul 21 at 3:52




x^3 = 3x^2. Would f go away and all there would be is 1?
– carter
Jul 21 at 3:52


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