Don't solving this problem, just need some info.

  • MHB
  • Thread starter Nate Learning
  • Start date
In summary, you could start by squaring both sides to get rid of the radical on the left and then use the chain rule to differentiate both sides with respect to $x$. However, it may be easier to just differentiate the equation as it is written.
  • #1
image0.jpg


Should I start off by squaring both sides to get rid of the radical on the left? and then start the derivative process? Thank you.
 
Physics news on Phys.org
  • #2
Looking at the square of the right side, i probably would not.
 
  • #3
Nate Learning said:
View attachment 11217

Should I start off by squaring both sides to get rid of the radical on the left? and then start the derivative process? Thank you.
You certainly could do it that way, but I don't see that it would be any easier than just differentiating the equation as it stands. Write it as $$\bigl(3x^7 + y^2\bigr)^{1/2} = \sin^2y + 100xy,$$ and differentiate both sides with respect to $x$ using the chain rule.
 
  • #4
Beer induced query follows.
Nate Learning said:
View attachment 11217

Should I start off by squaring both sides to get rid of the radical on the left? and then start the derivative process? Thank you.
From which book did you get this challenging derivative?
 
  • #5
$(3x^7+ y^2)^{1/2}= sin^2(y)+ 100xy$

The derivative of $3x^7+ y^2$ with respect to x is $21x^6+ 2y\frac{dy}{dx}$ so the derivative of $(3x^7+ y^2)^{1/2}$ is $\frac{1}{2}(3x^7+ y^2)^{-1/2}(21x^6+ 2y\frac{dy}{dx})$.

The derivative of $sin^2(y)$ with respect to x is $2 sin(y) cos(y)\frac{dy}{dx}$.

And the derivative of $100 xy$ with respect to x is $100y+ 100x\frac{dy}{dx}$.

So the derivative of $(3x^7+y^2)^{1/2}= sin^2(y)+ 100xy$ with respect to x is $\frac{1}{2}(3x^7+ y^2)^{-1/2}(21x^6+ 2y\frac{dy}{dx})= 2 sin(y) cos(y)\frac{dy}{dx}+ 100y+ 100x\frac{dy}{dx}$.

Solve that equation for $\frac{dy}{dx}$.
 

What is the purpose of "Don't solving this problem, just need some info."?

The purpose of this statement is to gather information about a problem without actually solving it. This may be done for various reasons, such as understanding the scope of the problem or identifying potential solutions.

Why would someone not want to solve a problem?

There are several reasons why someone may not want to solve a problem. It could be because they do not have the necessary resources or expertise, or they may not have the time or motivation to solve it. In some cases, the problem may also be too complex or difficult to solve.

What type of information is typically needed when "Don't solving this problem, just need some info."?

The type of information needed can vary depending on the problem at hand. It could include details about the problem itself, such as its cause, impact, and potential solutions. It could also involve gathering data or conducting research to better understand the problem.

Is it important to gather information before solving a problem?

Yes, it is important to gather information before solving a problem. This allows for a better understanding of the problem and its potential solutions. It also helps to identify any potential obstacles or challenges that may arise during the problem-solving process.

How can gathering information help in solving a problem?

Gathering information can provide valuable insights and perspectives that can aid in solving a problem. It can help to identify patterns, trends, and potential solutions that may not have been apparent before. Additionally, having a thorough understanding of the problem can lead to more effective and efficient problem-solving strategies.

Suggested for: Don't solving this problem, just need some info.

Replies
2
Views
842
Replies
2
Views
938
Replies
6
Views
1K
Replies
8
Views
195
Replies
9
Views
2K
Replies
1
Views
840
Replies
3
Views
1K
Replies
1
Views
877
Replies
8
Views
1K
Back
Top