Let z = f(x, y), u = x^2 + y^2 and \ v = 4xy \\ Find \frac { \partial x}{\partial u}, \frac...


Let {eq}z = f(x, y), \: u = x^2 + y^2 {/eq} and {eq}v = 4xy. {/eq}

Find {eq}\displaystyle\frac { \partial x}{\partial u}, \: \frac {\partial x}{\partial v}, \: \frac {\partial y}{\partial u}, \: \frac {\partial y}{\partial v} {/eq}

Partial Derivative:

To find the derivative of the partial derivative of several variables with respect to one of the variable. To find the partial derivative of one of the variable the other variables treated as constant.

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

Given: {eq}z = f\left ( x, y \right ), u = x^2 + y^2 and v = 4xy {/eq}

Find the value of {eq}\frac { \partial x}{\partial u} {/eq}.

{eq}\frac {...

See full answer below.

Learn more about this topic:

Partial Derivative: Definition, Rules & Examples


Chapter 18 / Lesson 12

What is a Partial Derivative? Learn to define first and second order partial derivatives. Learn the rules and formula for partial derivatives. See examples.

Related to this Question

Explore our homework questions and answers library