- #1
Nate Learning
- 2
- 0
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.
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.
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.
- #2
skeeter
- 1,103
- 1
Looking at the square of the right side, i probably would not.
- #3
Opalg
Gold Member
MHB
- 2,778
- 13
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.Nate Learning said:
- #4
jonah1
- 107
- 0
Beer induced query follows.
From which book did you get this challenging derivative?Nate Learning said:
- #5
HOI
- 921
- 2
$(3x^7+ y^2)^{1/2}= sin^2(y)+ 100xy$
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 $\frac{dy}{dx}$.
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 $\frac{dy}{dx}$.
FAQ: Don't solving this problem, just need some info.
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.