x^3 y5 - root x sin 3y = 400,000, find dy/dx

U

ugu

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QUESTION:
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My complicated solution. I wish to have a simplified one. THanks
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I have trouble reading your picture. I do not understand your second line. How does that come out of the product rule?

[math]\dfrac{d}{dx}(x^3y^5) = 3x^2y^5 + 5x^3y^4 * \dfrac{dy}{dx}[/math]
 
JeffM said:
I have trouble reading your picture. I do not understand your second line. How does that come out of the product rule?

[math]\dfrac{d}{dx}(x^3y^5) = 3x^2y^5 + 5x^3y^4 * \dfrac{dy}{dx}[/math]
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Exactly why it is complicated to me too. It seem longer than expected
 
Well, I cannot explain your work to you. How did you get that?
 
What about this?
 

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ugudansam said:
What about this?
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No. When you differentiate a function of y against x, you must use the chain rule. So dy/dx is going to be a factor wherever you differentiate a function of y. Implicit differentiation is a special case of the chain rule

[math]x^3 * (5y^4) * \dfrac{dy}{dx} + 3x^2y^5 - \dfrac{sin(3y)}{2\sqrt{x}} - 3\sqrt{x} * cos(3y) * \dfrac{dy}{dx} = 0.[/math]
Now solve for dy/dx.
 
JeffM said:
No. When you differentiate a function of y against x, you must use the chain rule. So dy/dx is going to be a factor wherever you differentiate a function of y. Implicit differentiation is a special case of the chain rule

[math]x^3 * (5y^4) * \dfrac{dy}{dx} + 3x^2y^5 - \dfrac{sin(3y)}{2\sqrt{x}} - 3\sqrt{x} * cos(3y) * \dfrac{dy}{dx} = 0.[/math]
Now solve for dy/dx.
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Meaning the second solution is also not correct?
 
ugudansam said:
Meaning the second solution is also not correct?
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Meaning the second solution is not correct.

Why do you say that this is not a problem in implicit differentiation?

What is the name of the topic under which you found this problem?
 
JeffM said:
Meaning the second solution is not correct.

Why do you say that this is not a problem in implicit differentiation?

What is the name of the topic under which you found this problem?
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Implicit and parametric differentiations
 
I do not know actually what this course is doing in computer science. I am not assimilating at all. Always lost along the line but I wish to know
 
ugudansam said:
I do not know actually what this course is doing in computer science. I am not assimilating at all. Always lost along the line but I wish to know
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1) Since it is under the implicit differentiation section, implicit differentiation is implied in the direction.
2)Calculus is fundamental for all STEM majors
3) Break the problem into smaller pieces
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BigBeachBananas said:
If the question doesn't ask you to do implicit differentiation, then why are you doing it? Treat y as a constant when differentiating.
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I am sorry to jump in the middle of the discussion, but your response attracted me. Is it really that we can solve this problem without using implicit differentiation? From my knowledge, if we can't solve for \(\displaystyle y\), then we don't have any other option than using implicit differentiation. If you can solve this problem without using implicit differentiation, please enlighten me.
 
nasi112 said:
I am sorry to jump in the middle of the discussion, but your response attracted me. Is it really that we can solve this problem without using implicit differentiation? From my knowledge, if we can't solve for \(\displaystyle y\), then we don't have any other option than using implicit differentiation. If you can solve this problem without using implicit differentiation, please enlighten me.
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In multivariable calculus, if such a problem were presented, it's a partial derivative. https://www.mathsisfun.com/calculus/derivatives-partial.html
 
BigBeachBananas said:
In multivariable calculus, if such a problem were presented, it's a partial derivative. https://www.mathsisfun.com/calculus/derivatives-partial.html
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You mean that the question would be asking for

\(\displaystyle \frac{\partial f}{\partial y}\) or \(\displaystyle \frac{\partial f}{\partial x}\)

If this is the case, the question should be written as

Given that \(\displaystyle f(x,y) = 400000 + \sqrt{x} \sin 3y - x^3 y^5\), find \(\displaystyle \frac{\partial f}{\partial x}\) or even \(\displaystyle \frac{df}{dx}\).

But it was not. It is so clear that it is an implicit differentiation question.

Even if we assume that it is not an implicit differentiation question, \(\displaystyle \frac{dy}{dx}\), doesn't imply to treat \(\displaystyle y\) as a constant.
 
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