Can Implicit Differentiation Be Done by Separation of Variables?

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In summary, implicit and separate refer to different types of methods used in experiments or studies. Implicit methods are implied or understood without being directly stated, while separate methods are distinct or different from each other. The decision to use these methods depends on the research question and variables being studied, and they can also be used together for a more comprehensive understanding. However, there may be drawbacks to using these methods, such as difficulty in interpretation and limitations in capturing complex processes. To ensure validity and reliability, researchers can use multiple measures, conduct pilot studies, and consider potential biases in the study design.
  • #1
karush
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MHB
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$\tiny{s8.2.6.2}$
Find y' of $2x^2+x+xy=1
$\begin{array}{lll}
\textit{separate variables}
&xy=2x^2+x+1 \implies y=\dfrac{2x^2+x+1}{x}\implies 2x+1+x^{-1}
&(1)\\ \\
\textit{differencate both sides}
&y'=2-\dfrac{1}{x^2}
&(2)
\end{array}

ok it seems we can do any implicit differentiation by separation or not?
I think I got the right answer hopefully
 
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  • #2
watch those signs ...

$y=\dfrac{1-x-2x^2}{x} = \dfrac{1}{x} - 1 - 2x$

$y’ = -\dfrac{1}{x^2} - 2$
 
  • #3
skeeter said:
watch those signs ...

$y=\dfrac{1-x-2x^2}{x} = \dfrac{1}{x} - 1 - 2x$

$y’ = -\dfrac{1}{x^2} - 2$
yikes... ok
 

FAQ: Can Implicit Differentiation Be Done by Separation of Variables?

What is the difference between implicit and separate in S8.2.6.2?

Implicit and separate refer to two different ways of handling variables in the S8.2.6.2 section of a scientific study. In implicit, the variables are not explicitly stated but are rather implied or assumed. In separate, the variables are clearly defined and separated into distinct categories.

When should implicit be used in S8.2.6.2?

Implicit should be used when the variables are directly related and can be assumed to have an impact on each other. This can save time and effort in explicitly defining each variable and their relationship.

How is separate different from explicit in S8.2.6.2?

In S8.2.6.2, separate and explicit are similar in that they both involve clearly defining variables. However, explicit involves explicitly stating the relationships between the variables, while separate simply categorizes them without defining their relationships.

Are there any drawbacks to using implicit in S8.2.6.2?

One potential drawback of using implicit in S8.2.6.2 is that it may lead to assumptions being made about the relationships between variables, which could result in inaccurate conclusions. It is important to carefully consider the variables and their potential impact on each other before using implicit.

Can implicit and separate be used together in S8.2.6.2?

Yes, implicit and separate can be used together in S8.2.6.2. This may be beneficial in cases where some variables can be assumed to have an impact on each other, while others need to be clearly defined and separated. It is important to carefully consider the variables and their relationships before deciding on the best approach.

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