Purchase Solution

Partial differentiation

Not what you're looking for?

Ask Custom Question

When I write (Wx)y it means the partial derivative of W according to x with y constant !

Supposethat g(x,y)=c a constant and W=f(x,y,z) . Which of the following makes sense as the derivative Wx ? :

a) (Wx)x b) (Wx)y c) (Wx)z

2) suppose that cos(x-y)=5u and W=x^2*y*u. Find (Wu)x.

3) Consider the curve of points (x,y,z) satisfying
x^3-xyz=-1 and x^3+y^2*z^3-xz=7.
Use the method of differentials to find dz/dy at (x,y,z)=(1,1,2).

Purchase this Solution

Solution Summary

This solution shows how to use the method of differentials.

Solution Preview

1. (c) (Wx)z makes sense.
Since (Wx)z=(df/dx)+(df/dy)*(dy/dx)
But from g(x,y)=c, we can make derivative to x on both sides and get dg/dx+(dg/dy)*(dy/dx)=0, this implies dy/dx=-(dg/dx)/(dg/dy). So we plug it in (Wx)z=(df/dx)+(df/dy)*(dy/dx) and can find ...

Purchase this Solution

Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.