How to Solve for Jacobians and Pedal Form Equations in Scientific Notation

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In summary, the conversation discusses finding the solution to the equation y^2 = 4ax in pedal form. The individual asking for help mentions they have tried but could not solve it and asks for the solution to be sent if anyone has found it.
  • #1
ADITYABR
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I need the solution for this If u = 2yz/x, v= 3zx/y, w= 4xy/z Show that ∂(x,y.z)/∂(u,v,w) = 1/96. Please
 
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  • #2
What, exactly, is your difficulty? Do you know what the "Jacobian" is? Do you know how to find the partial derivatives.

Perhaps the difficulty is that you are given u, v, and w as functions of x, y, and z but are asked for [itex]\partial(x, y, z)/\partial(u, v, w)[/itex] rather than [itex]\partial(u, v, w)/\partial(x, y, z)[/itex]? Not to worry!
[tex]\dfrac{\partial(x, y, y)}{\partial(u, v, w)}= \dfrac{1}{\dfrac{\partial(u, v, w)}{\partial(x, y, z)}}[/tex]
 
  • #3
Yes I do know how to find. Yes I have given function w.r.t x, y, z as it was given in the problem to find the same as above. Thanks for the reply
 
  • #4
Excellent! Problem solved.
 
  • #5
I Need the solution to this equation y^2 = 4ax in pedal form? I tried but could not solve it . If anybody found it kindly send the answer and it would be great.
 

FAQ: How to Solve for Jacobians and Pedal Form Equations in Scientific Notation

What is the purpose of the Jacobian in these equations?

The Jacobian is a mathematical tool used to calculate the derivative of a multivariable function. In this case, it is used to find the partial derivatives of U and V with respect to x, y, and z.

How is the Jacobian calculated?

The Jacobian is calculated by taking the partial derivatives of the given equations with respect to each variable. In this case, the Jacobian would be a 3x3 matrix with the partial derivatives of U and V with respect to x, y, and z.

What information does the Jacobian provide?

The Jacobian provides information about the rate of change of a multivariable function. It can help determine the slope of a function at a certain point and the direction of the fastest change.

How is the Jacobian used in scientific research?

The Jacobian is used in many fields of science, particularly in physics, engineering, and mathematics. It is used to analyze and model complex systems, such as fluid dynamics, electromagnetism, and quantum mechanics.

Are there any limitations to using the Jacobian?

One limitation of using the Jacobian is that it assumes the function is differentiable at all points. If the function is not differentiable at a certain point, the Jacobian may not accurately represent the rate of change at that point. Additionally, it can be challenging to calculate the Jacobian for very complex functions.

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