# Solve Z = x^2y - 2xy^2 + y - 8 and y = 2x^2 +3/x

• Becky
In summary, the conversation is about finding dz/dx in terms of x and y given a complicated equation involving z and y as functions of x. Several attempts have been made, but it is a difficult problem. One person suggests using the chain rule and substituting the value of y in terms of x to solve. Another person offers a solution using the chain rule and correcting a potential mistake in the first person's solution. It is ultimately decided that the first person's solution is incorrect due to a mistake in the differentiation.
Becky
hay everyone...need some help on the question

I need to find dz/dx in terms of x and y, if:

Z = x^2y - 2xy^2 + y - 8 and y = 2x^2 +3/x!

tried solving it a few times, but its a difficult one! any help and working out would be great!

We'd be better able to help if you show us what you've done.

Ok dz/dx

x = 2y - 4y +y

y = 4x + 3

dont think that is right!

You are given z as a function of x and y, and y as a function of x. So I suggest that you substitute all the y int he equation of z for their value in terms of x and then calculate dz/dx.

Use the chain rule. Since y is a function of x, dz/dx= 2xy+ x2y'- 2y2+ 4xy6y' + y'. since y = 2x2 +3/x, you can find y' as a funcion of x and substitute.

hey,
i think i can help,dz/dx=x^2y[dy/dx(log[x^2])+2y/x]-2y^2-4xydy/dx+dy/dx
where dy/dx=4x - {3/x!}[1/x+1/x-1+1/x-2+1/x-3...]

hey
hallsofivy ur step was wrong since y is a function of x can't differentiate like that
check ur solution one more time,ur step will be right if the question reads x^2 times y ,but if it is x raised to the power of 2y then mine is correct.also i hope the 6 in the function 4xy6y' was a typing mistake cos if it is not then ur answer is wrong.

## 1. What is the purpose of solving this equation?

The purpose of solving this equation is to find the values of x and y that satisfy the given equations. These values can then be used to further analyze and understand the relationship between the variables x and y.

## 2. How do you solve this equation?

To solve this equation, we can use substitution or elimination. First, we can rearrange one of the equations to solve for one variable in terms of the other. Then, we can plug this expression into the other equation and solve for the remaining variable. Finally, we can substitute the value of this variable into one of the original equations to solve for the other variable.

## 3. Can this equation have more than one solution?

Yes, this equation can have multiple solutions. Since there are two variables, there can be an infinite number of combinations of x and y that satisfy the equations. It is important to check the solutions obtained to ensure they are valid for the given equations.

## 4. What type of graph does this equation represent?

This equation represents a curve in a 3-dimensional space. Since there are two variables, x and y, the graph would be a surface in a 3D coordinate system. This can be visualized using a graphing calculator or computer software.

## 5. Can this equation be solved using any other methods?

Yes, this equation can also be solved using numerical methods such as Newton-Raphson or bisection method. These methods involve using an initial guess for the values of x and y and iteratively improving the solution until it converges to the correct values. However, these methods may not always give an exact solution and may require multiple iterations.

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